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Heat treatment is typically a method for strengthening materials, but it can also change some mechanical properties, such as improved formability and machining. The process is most commonly used in metallurgy, but heat treatment is also used in the manufacture of glass, aluminum, and steel. Web Industries takes the mystery out of commercializing your medical devices. Our automated high-volume IVD and LFI manufacturing, assembly, and packaging solutions make the pain of bringing your tests to market disappear.

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Electropolishing is an electrochemical process similar to electroplating, but in reverse. Electropolishing smooths and streamlines the microscopic surface of a metal object, such as , or series stainless steel. The resulting surface is microscopically featureless, with no torn surface remaining.

In electropolishing, material is removed ion by ion from the surface of the metal being polished. The fundamental principles of electrolysis and electrochemistry replace traditional mechanical finishing techniques, including grinding, milling, blasting, and buffing as the final finish.

In basic terms, the metal object to be electropolished is immersed in an electrolyte and subjected to a direct electrical current. The metal object is maintained anodic, with the cathodic connection being made to a nearby metal conductor. In addition, the polarized surface film is exposed to the combined effects of oxygen gassing. This occurs with the removal of electrochemical metal, saturation of the surface with dissolved metal, and the agitation and temperature of the electrolyte.

What are minimally invasive devices? Minimally invasive surgery refers to surgical techniques that limit the size of incisions needed, or has a short recovery time. When a medical device is placed within a patient during such a surgery, it is a minimally invasive device. Many procedures involve the use of arthroscopic or laparoscopic devices, and remotecontrol manipulation of instruments with indirect observation through an endoscope or large display panel.

The surgery is usually carried out through the skin or through a small body cavity or anatomical opening and can involve a robot-assisted system. What is single-use manufacturing? Single-use manufacturing, or more clearly manufacturing single-use devices, emerged about the mids and stemmed from single-use systems which were gaining wider use in the pharmaceuticals industry, in particular for the production of specialized drugs.

Single-use manufacturing now involves the production of relatively complex disposable devices used in surgical procedures such as electrosurgery. Razor blades and their holders are another example. Such devices are usually complex items intended for a single use, as opposed to simple disposables. They are examples of relatively simple singleuse products. At first, the bags replaced glass bottles and soon became available with a plastic tube or two, connectors, valves, and vials for taking samples.

More complex disposable products are used in systems for specialized or boutique drug production and may include disposable filters, electronics, and sensors. The alternative to single-use systems, to follow the drug example, would be processes made of relatively inflexible stainless-steel vessels and reactors, hard piping, valves, and so on. Such a fixed system must be cleaned and sterilized, a relatively labor- and energy-intensive operation.

Single-use devices, by one calculation, are more cost-effective and faster to implement. Other advantages of single-use systems include: www. They reduce capital expenditures and require less facility space. Single-use systems are adaptable to patient-proximity manufacturing, a consideration for epidemic and bioterrorism vaccine deployment.

Single-use systems reduce the need for the steam, hot water, ultra-pure water, and chemicals used to clean stainless steel components, and eliminate the need to revalidate conventional equipment. Single-use systems reduce the possibility of cross contamination while improving sterility assurance.

More qualified vendors are ready to provide timely supply and service of components and systems. Less time is spent in changeovers for batch-to-batch and product-to-product. In addition, some single-use systems are delivered gamma-sterilized and pre-qualified by the supplier. What do ratcheting devices do on surgical tools? A ratchet mechanism on a medical tool is a step-locking device.

In one application, as the handles of a clamping mechanism are closed, its jaws also close and the ratchet holds them in a locked position. The ratchet consists of a notched bar on each handle, the notches facing and overriding when the handles are closed. What methods are used to join materials? The joining of materials is an important technology in many manufacturing industries. Most products, machines or structures are assembled and fastened from parts, and the joining of these parts may be achieved through rivets, seaming, clamping, soldering, brazing, welding and the use of adhesives.

With continuing advances in the medical industry, medical devices are becoming increasingly complicated. Such devices are usually comprised of components and materials that must be joined in some way, whether used outside the body, in the case of instruments and surgical tools, or inside the body, for diagnostic or therapeutic purposes.

To create highly reliable devices, one must choose which joining process is appropriate at every step. Many factors influence those choices, from production economics, to mechanical properties such as strength, vibration damping and durability, corrosion or erosion resistance, as well as the ability to correct defects. Joining processes are typically divided into three categories: Mechanical joining, welding, and adhesive bonding. Medical devices are manufactured using a variety of materials, from metals to polymers to ceramics, and can be joined using all three methods.

Mechanical joining is a process for joining parts through clamping or fastening using screws, bolts or rivets. Advantages of mechanical joining include versatility, ease of use, and the option to dismantle the product in cases where regular maintenance requires it. The ability to join dissimilar materials is another benefit. A drawback of using mechanical joining is the lack of a continuous connection between parts, because the joint is achieved through discrete points.

Also, holes created for joining are vulnerable to fractures and corrosion. Welding includes fusion welding, brazing and soldering, and solid-state welding. In fusion welding, melting and solidification occur in the zone being joined.

For metals and plastics, both the work pieces and the filler material experience melting. Brazing and soldering join materials by adding a melted filler material between the joined surfaces. Solid-state welding requires no melting of base of filler materials, because it only involves plastic deformation and diffusion. Adhesive bonding joins parts using bonding chemicals.

This process may be used to join polymers and polymermatrix composites, as well as polymer-to-metal, metal-to-metal, and ceramic-to-metal. In this method of joining, joints can withstand shear, tensile and compressive stresses, but do not have good resistance to peeling.

What is contract manufacturing? Contract manufacturing is a process that establishes a working agreement between two companies. As part of the agreement, one company custom-produces parts or other materials on behalf of the client. In most cases, the manufacturer also handles ordering and shipment schedules. As a result, the client does not have to maintain manufacturing facilities, purchase raw materials, or hire labor to produce the finished products.

The basic working model used by contract manufacturers translates well into many different industries. There are many contract manufacturers in pharmaceuticals, as well as food production, and the creation of computer components and other forms of electronics. Even industries such as personal care and hygiene products, automotive parts, and medical supplies are often produced under the terms of a contract-manufacturing agreement.

What are electromechanical devices? Almost any single device with an electrical and mechanical component can be referred to as electromechanical EM. You might even call an electric motor an electromechanical device, because it turns electricity into rotary mechanical motion. Also, a controller somewhere in the design governs the functions of the EM device. A brief Controller section accompanies this discussion. Presently, few EM devices, other than mechanical hearts or cardiac assist devices, are implantable, but that will change.

A trend in the design of a few EM devices is toward miniaturization, to make them as unobtrusive as possible, either for healthcare setting or as wearable units. Exploring a few examples of EM devices can sketch the landscape of the variations available.

Consider a particular AC-powered electric actuator that operates from to Vac. It comes with positioning electronics to define the limits of the motion that are UL Listed, which means that device meets UL safety standards.

The actuators combine a brushless servomotor with either rotary or linear output actuation and digital position control. Electromechanical cylinders although they are not cylindrical give users control over positioning accuracy, axial thrust, torque, and speed, providing more flexibility to applications that traditionally use hydraulic or pneumatic cylinders.

The devices use a precision-rolled, ball-screw actuator that ensures high positioning accuracy and repeatability, and eliminates the stick-slip effect. To give an idea of what is available from such cylinders, the units from one manufacturer come in six sizes with stroke lengths to 2,mm and speeds to 1. Each unit is rated to an IP65 level of protection. As you can imagine, the quality of EM devices spans a range. Those with a rating of IP65 International Protection are protected against solids, objects, and water.

The 6 indicates protection against dust, while the 5 indicates protection against liquids and low-pressure jets of water from all directions. A second example of an EM device is a linearactuator line that includes explosion-proof devices. The linear actuator meets ATEX EU directives for explosion-proof equipment requirements for use in potentially explosive atmospheres, such as high-oxygen areas.

These servo-electromechanical systems are said to offer a clean, fast, simple, and cost-effective alternative to hydraulics and longer life compared to pneumatics. For a third example, consider the gripper, a device often used with pick-and-place robotic systems. Fingered tooling, or jaws, attach to the grippers to hold an object. They come in a variety of styles and powered designs.

Three common types are parallel two-fingered , three-fingered, and angled designs. The most common are parallel designs, with two fingers that close on a workpiece to grip it, or open out to create contact friction on an inside surface.

Three-finger designs hold the workpiece in the center. What is product development? Product development is the process of designing, creating, and marketing a product. The procedure mainly focuses on developing systematic methods for guiding all the processes involved in getting a cutting-edge product to market.

The product development process can involve improving an existing. Continual product development is necessary for companies striving to keep up with innovation and technology to ensure future profitability and success. Interchangeable with our original E4P optical kit encoders Transmissive optical design Patent pending codewheel design Customizable options to fit your needs.

The E4T miniature transmissive optical encoder is designed to provide digital quadrature encoder feedback for high volume, limited space applications. It utilizes an innovative, push-on codewheel patent pending which accepts shaft diameters of 2.

What are motion controllers? A motion controller governs the motion and position of an object on a machine axis. A properly functioning machine also requires motors or fluid-power cylinders for motive power, sensors for judging position and speed, a computer to store and execute rules that govern the motion and other conditions, and a network for taking in sensor signals and outputting command signals.

For further discussion of linear guides, motors, and sensors, see the accompanying sections. Motion controllers are often implemented using computers, but it is also possible to control motion with analog devices. Most medical applications for motion controllers are on manufacturing equipment and patient-assist devices. A simple and inexpensive controller might be a single-chip microcontroller running a real-time operating system.

Windows-based application development software may provide a setup wizard to shorten installation and evaluation time. This could be appropriate for a simple one- or two-axis medical device. A large manufacturing machine, however, would require something that can handle more inputs, make decisions quickly, and provide appropriate outputs, such as alarms when something goes wrong. The variety of available controllers is considerable. At the physical level, most motion controllers are stand-alone versions based on PCs, or are microcontrollers built into equipment.

Stand-alone controllers are complete systems that include all electronics, power supplies, and external connections which all mount in a physical enclosure. PC-based controllers can resemble the motherboard of a basic personal computer or a ruggedized industrial PC,. In addition, the controller interfaces with lab and clean-room devices, and other equipment. One big plus for PC-based controllers is that they provide a readymade graphical user interface for easier programming and tuning. Another type of controller typically handles simple motion along a few axes.

The latter can be anything from a single keypad or a touchscreen, to an Ethernet connection with a PC for more complex programming. No matter its form, the PLC is programmed through the user interface. The PLC consistently scans through all its inputs, looking for changes, then updates its outputs depending on commands in its programming.

This usually takes only a few milliseconds; faster scan times accommodate processes with more real-time demands. What are electric motors?

An electric motor is an electrical machine that converts electrical energy into mechanical energy. In certain applications, such as in the transportation industry with traction motors, electric motors can operate in both motoring and generating or braking modes to also produce electrical energy from mechanical energy.

Electric motors can be powered by direct-current DC sources, such as batteries, motor vehicles, or rectifiers, or by alternating-current AC sources, such as from the power grid, inverters, or generators.

Small medical motors are found some active prosthetics and lab equipment. Generalpurpose motors with highly standardized dimensions and characteristics provide convenient mechanical power for industrial use. The largest of electric motors are used for ship propulsion, pipeline compression, and pumpedstorage applications with ratings reaching megawatts. Electric motors may be classified by electric power source type, internal construction, application, type of motion output, and other characteristics.

Assemble your individual maxon DC drive: You can onfigure the gear stages, the motor bearings, the shafts, the encoder and much more. Design your custom drive online today and your finished drive will ship from Switzerland in 11 working days. Contact us at info maxonmotorusa. What are AC motors?

Motors powered by alternating current are considerably different from those powered by direct current DC. AC motors come in a variety of designs, but each has two major components: The stator or stationary parts and the rotor or rotating components. The stator is made of sheet-steel laminations. The slotted inner surface holds coil windings that induce the magnetic forces that turn the rotor. Because brushless AC motors have no commutators or brushes, they require less maintenance than brushed DC motors.

DC motors are controlled by varying voltage and current. With AC motors, voltage and frequency along with the number of magnet poles control the motor speed. There are two fundamental types of AC motors: induction and synchronous.

In induction motors, the rotor turns in response to the induction of a rotating magnet field within the stator. The most common design for AC induction motors is the squirrel-cage configuration, consisting of two rings, one at each end of the motor, with bars of aluminum or copper connecting the two ends.

The properties of induction motors make them suited to several medical applications. For instance, they are simple, rugged, and easy to maintain.

They also run at constant speed across a range of loads, from zero to full load. Their only drawback is that they are generally not amenable to speed control, although the availability of sophisticated, usually three-phase, variable frequency drives means that even induction. Synchronous motors are so named because they run synchronously with the frequency of the source.

The motor speed is fixed and does not change with load changes or voltage. These motor are mostly used where precision and constant speed are required.

Most synchronous motor are used in heavy industrial applications. Because DC motors use permanent magnets, no energy is used to generate the magnetic field, as with AC motors. The energy used by AC motors to create the magnetic field decreases their efficiency compared to DC motors.

The frequently encountered National Electrical Manufacturer Assn. NEMA and its classifications are a further way to characterize motors and size. For instance, a NEMA 1 motor is best used indoors and has some protection against falling dirt. A NEMA 13 refers to a motor enclosure constructed for indoor use to provide some protection to personnel against access to hazardous parts.

NEMA 23 refers to a mounting area of 2. What are gearmotors? Gearmotors are motive-force systems consisting of an electric motor and a reduction gear train, combined into one easy-to-mount and configure package. This greatly reduces the complexity and cost of designing and constructing power tools, machines, and appliances calling for high torque at relatively low shaft speeds or rpm.

Gearmotors allow the use of economical, lowhorsepower motors to provide great motive force at low speed, such as in lifts, winches, medical tables, jacks, and robotics. They can be large enough to lift a building or small enough to drive a tiny clock. M www. It allows device monitoring and communication between nodes or motors. ISO Harmonizes medical device regulatory requirements for quality management systems. It includes particular requirements for medical devices and excludes some requirements of ISO that are not appropriate as regulatory requirements.

NEMA A motor with a 1. It is not a power indicator. N-cm: Newton-centimeter, a torque unit and a unit of force applied at a distance from a rotary axis. They are more efficient than brushed motors because they have less internal friction.

Better yet, they usually last longer and expose their surroundings to less electromagnetic interference. Brushless DC motors are suitable in low-power applications, such as consumer products, as well as high-power uses. The design, however, is slightly more expensive than a similarly rated brushed DC motor. All DC motors generate a magnetic field, whether with electromagnetic windings or permanent magnets.

An armature, which is often a coil of wires, is place between the north and south poles of a magnet. When current flows through the armature, the field produced by the armature interacts with the magnetic field from the magnets and generates torque and, from that, rotary motion. The coil windings produce a rotating magnetic field because they are separated from each other electrically, which allows them to be turned on and off.

A sampling of recent BLDC motor announcements reveals a fast pace of evolution. For instance, one manufacturer has unveiled its smallest DC brushless motor yet.

With a 4mm diameter, the motor comes in two different lengths. Certified to ISO , the brushless micro drive is useful in medical applications. The manufacturer says it has no common wear parts, such as brushes or commutators, so is highly reliable. For higher-torque applications, many manufacturers offer gearboxes or speed reducers that mate neatly with their motors. This allows connecting multiple brushless motors built with the same networking protocol to various components in a system, reducing wiring and installation costs while increasing system communications and integrity.

The CANopen interface allows connecting up to brushless DC motors with a single, shielded two-wire cable. Data may be transmitted at speeds up to kBd and over yards.

At lower baud rates, the transmission distance can exceed three miles, making communications flexible to almost any location. Another manufacturer offers a high-torque density motor as an economical yet higher-performance, general-purpose servomotor. Its NEMA 17 mounting configuration is adaptable to most metric mounting requirements, making it an easy upgrade for many stepper motor applications.

The motor comes in three lengths with a continuous torque range of 11 to 31 Ncm and a peak torque range of 35 to 99 Ncm. CGI precision gearheads and custom assemblies are used in medical applications ranging from cardiac support to medical robotics. Your custom gearbox solutions are CGI standard products. CGI Motion standard products are designed with customization in mind. We understand most off-the-shelf products or a complete inhouse design may not fit your application, so our standard products are designed for functional flexibility.

Our team of experts will work with you on selecting the optimal base product and craft a unique solution to help differentiate your product or application. So when you think customization, think standard CGI gearbox assemblies.

Connect with us today to explore what CGI Motion can do for you. What is linear motion? Linear motion, as you would expect, is motion in a line. But keeping a load moving in a line and stopping where needed is much more interesting. Briefly, it involves linear guides, actuators, sensors, and controllers. This article briefly introduces the first two items.

Linear guides, for instance, are devices used to keep loads moving in one direction. They come in a wide variety of lengths, widths, load capacities, and bearing designs. Linear guides usually consist of a stationary component, a track, and a load-carrying part a carriage riding on bearings. The bearings can be plain or use rolling elements.

Linear motion components are used in a variety of precision applications, from the light loads of medical equipment to heavy loads of machine tools. Plain-bearing linear guides, the simplest design, have no moving parts and rely on low-friction sliding surfaces to smoothly move on their rails.

In contrast, the more common rolling-element. Rolling element-based linear guides are further categorized as either recirculating element or guide wheel. In a re-circulating design, rolling elements are contained in circuits in the carriage and continuously circulate within the circuit when the guide block moves.

An alternative design uses rolling-element bearings with special circumferential profiles that let them roll on rails with complementary profile surfaces.

The most common profile sets are V-wheels with a V-shape profile that matches a V-rail. Guide wheels use rolling elements contained within circular circuits to support loads. With these features, a linear guideway can provide greater precision than plain bearings.

Linear actuators The carriage is moved using a wide variety of drives. Motion may come from a lead screw, a ball screw, a belt drive, or a linear motor.

See the following sections for more on each of these. Trends in linear motion While there are several trends in this industry segment, two that stand out are at opposite ends: Miniaturization and the creation of the most complete systems. Both should interest medical device designers. Miniature-motion slides let devices make fine adjustments, often 0.

Such a carriage on a linear guide with manual drive would let lab workers position a specimen under a microscope and move it around in small, precise increments. At the other end of trend scale, more complete units can include x, y, and z axes driven by servomotors with an accompanying controller programmed through a user interface. For more information on Machined Springs, including custom applications, go to MachinedSprings. What are linear motors? Linear motors produce linear motion, not rotary motion, as do most motors.

Like many rotary motors, linear motors consist of a coil primary part or forcer and magnets secondary part. Although there are many types of linear motors, brushless ironcore and ironless designs prevail in automation and positioning applications.

Each has special construction features and performance characteristics. Linear motors offer several advantages over belts, screws, and other drive mechanisms, including almost unlimited lengths, low maintenance, and higher accuracy and repeatability.

There are no mechanical-transmission components — such as pulleys, couplings, or gearboxes — to introduce elasticity and backlash. The lack of rotating or sliding components also means linear motors are almost maintenance-free, with only the support bearings linear guides requiring periodic maintenance.

Linear motors can also provide unlimited travel by simply stacking magnet tracks end-to-end. And with the ability to use more than one primary part on a single secondary part, systems can be built with multiple carriages performing independent movements, simplifying the system design and reducing space.

Manufacturers have various ways of reducing the cogging effect. Ironless linear motors eliminate iron from the primary by using coils embedded in an epoxy plate.

This reduces mass and lets them achieve highly dynamic motion. Where iron core linear motors consist of a flat magnet track, ironless linear motors typically consist of a U-shaped magnet track, with two plates of magnets facing each other.

This reduces heat dissipation and means that ironless linear motors have lower thrust forces than iron core motors. But their lower mass due to a lighter primary part gives them better acceleration and short settling times, making them ideal for precise, rapid movements. Another plus for ironless versions: No attractive forces between the primary and secondary parts, because there is no iron in the primary. This makes them easier and safer to assemble than ironcore linear motors.

It also means that the supporting bearings need not be sized to accommodate the attractive forces, and will generally have a longer service life. Ironcore linear motors, as their name suggests, are constructed with the coils of the primary wrapped around an iron core.

The secondary part is typically a stationary, flat magnet track. Ironcore linear motors are characterized by their high continuous force and ability to move large loads, which make them ideal for machine tool, injection molding, and pressing applications.

One downside of ironcore linear motors is an effect known as cogging, which is caused by the magnetic pull of the secondary on the primary as it. What are leadscrews? A positioning device without a linear motor is likely to use a leadscrew or a ball screw discussed in an accompanying section.

The leadscrew or power screw is a threaded shaft on which rides a simple threaded nut. It has no ball bearings. Leadscrews use the helix angle of the thread to convert rotary motion to linear motion. The nut attaches to a load a movable table or carriage so that, as the shaft turns, the nut and load transits one way or the other.

This simple design is open to wide variations, such as length, thread pitch, coating, and nut design. The shaft can be turned by any of the motors discussed in another section. With attention to selection and application, leadscrews can work with the efficiency that comes close to ballscrews on many applications — as well as high load capacity and positioning accuracy.

In addition, engineers can more easily tailor leadscrews to an application, thanks to a flexible configuration and form factor, the ability to operate without lubricant, quieter operation, and lower cost. Leadscrew performance depends heavily on the coefficient of friction between the nut and screw, which in turn depends upon the materials of the nut and screw.

Leadscrews typically use nuts made of internally lubricated plastic or bearing-grade bronze. Plastic nuts usually travel on stainless-steel screws, while bronze nuts often run on carbon-steel screws. A few simple steps can help determine whether or not a leadscrew is a good fit for an application and select the most appropriate leadscrew features.

Leadscrew load capacity: When considering whether leadscrews or ballscrews are better for an application, look at the required load capacity.

Plastic nuts are suitable for light loads of less than lb, although plastic nut designs for lb and beyond are possible. Bronze nuts, on the other hand, are useful for much heavier loads. Helix angle is the. It is the angle of the advancement of the thread. As a general rule, higher helix angles mean higher efficiency.

A higher helix angle is more efficient because less of the energy driving the leadscrew goes into overcoming friction. This is because the number of times the screw must rotate to get a given linear displacement is lower on a high helix screw.

One disadvantage of a high-helix angle is that it necessitates more torque to turn the screw. Leadscrew speed: Leadscrews come in leads from less than 0. This range can deliver jog speeds to 70 in. This leadscrew feature can provide advantages in many applications. For example, devices that must accurately position payloads can use a leadscrew with a low helix angle to get high positioning resolution.

Other applications benefit from fast jog speeds and low screw rpm, providing quiet operation and long life. The maximum rotational speed of a leadscrew is limited by the critical speed of the screw — the speed at which resonance occurs.

Leadscrew nuts can be driven at high rpm, but depending on the applied load, heat buildup may limit duty cycles. What are actuators? An actuator is a device that converts energy into motion or applies force. The mechanical device takes energy in the form of hydraulics, pneumatics, or from a motor, and converts it into motion. That motion can come in many forms, such as ejecting, blocking, or clamping. Actuators are used in manufacturing applications such as switches, pumps, motors, and valves.

What are ball screws? A ball screw, like a lead screw, converts rotary motion into linear motion. The device consists of a threaded shaft and a ball nut. The latter device rides on the screw, supported by a series of ball bearings that provide a rolling surface rather than the sliding surface of a lead screw.

The balls roll between the nut and shaft. Because there is no sliding motion, ball screws run more efficiently than lead screws. This is their great advantage. Ballscrews are often a first choice for linear-motion applications because the use of recirculating ball bearings provides high efficiency, load capacity, and positioning accuracy.

Furthermore, ballscrews generally provide equal or better load capacity than One drawback to ballscrews is that they require high levels of lubrication. Ballscrews should always be properly lubricated with a proper formulation to prevent corrosion, reduce friction, ensure efficient operation, and extend operating life.

Backlash, that little bit of play between several mechanical components, can be eliminated with preloading. A few ballscrew terms, such as circuits, turns, lead, pitch, and starts, are widely used — and misused — terms that quantify various aspects of ball screw assemblies.

Although these terms are related, each has a unique meaning and significance to ball-screw design and performance. Lead and pitch are related but different specifications. Lead refers to the linear distance traveled for each complete turn of the screw, while pitch is the distance between screw threads. These terms are often used interchangeably, and for singlestart screws lead and pitch are equivalent. However, lead and pitch are not equal for screws with multiple starts. Ballscrews are commonly available in medium leads between 0.

Considering the geometry of a screw assembly, it makes sense that as the lead of the screw becomes larger, the number of tracks inside the ball nut becomes smaller, so fewer balls are carrying the load.

While larger lead screws offer longer travel per revolution and higher speeds, their ability to provide a high load capacity is compromised. In theory, the number of ball tracks could be increased by making the ball nut longer, but manufacturing constraints and limits on ball nut length make this an impractical solution. Circuits and turns are also related concepts. A ball circuit is a closed path of recirculating balls. The relationship between circuits and turns is influenced by the recirculation method.

Ball returns that use the deflector or thread-to-thread aka cross-over method recirculate each turn of balls individually. Therefore, the number of turns is equal to the number of circuits. When balls are returned by an internal channel or an external tube, the recirculating balls can cross several threads, so one circuit can have multiple ball turns.

That is, the balls make several trips around the screw shaft before being recirculated. Multi-start ball screw assemblies typically use the internal channel method of recirculation pictured.

These can be designed for multiple circuits, by incorporating more than one internal recirculation channel in the nut body. What are seals?

Seals, important components in many medical devices, are used to isolate and sometimes transmit fluids and gases. They are also occasionally used to provide structural support for other components of the device. Static seals range from basic O-rings to complex shapes and can be found in medical devices ranging from pumps and blood separators to oxygen concentrators. They let a spinning shaft pass through the inside dimension of the O-ring.

Motorized systems, such as scanning devices, require rotary seals. In these applications the important consideration is heat from friction where the rotating component meets the seal material. We love a good challenge. If you need a fluid handling component for whatever reason, no matter how extreme, talk to The Lee Company.

Our extensive family of precision fluid control products offers unsurpassed reliability in just about every configuration you could imagine, including:. A Lee engineer will be happy to discuss your application, and develop a custom design if needed. Whatever problem you face, make the solution easy. Contact The Lee Company today.

What is a valve? A valve is a device that controls the passage of fluid through a pipe or duct, especially a device that allows movement in one direction only. A common example of such a valve in a medical context is a replacement heart valve.

In most cases, heart-valve replacement is an open heart operation. The new artificial usually a prosthetic valve is then sewn into place. In paitents too sick to undergo surgery, the valve can be replaced via catheter without opening the chest. What is a pump?

A pump is a mechanical device that uses suction or pressure to raise or move liquids, to compress gases, or to force air or gases into inflatable objects, such as balloon catheters.

The most common pump used in medicine is the external infusion pump. There are many different types of infusion pump, used for a variety of purposes and in different environments. Infusion pumps may be capable of delivering fluids in large or small amounts and may be used to deliver nutrients or medications, such as insulin or other hormones, antibiotics, chemotherapy drugs, and pain relievers.

Portable or wearable versions are called ambulatory infusion pumps. The pump is equipped with a feature. Insulin pumps are frequently used in the home.

What is a peristaltic pump? Peristaltic pumps generate fluid flow in a tube through the use of external, rotating rollers. These rollers are mounted on a rotor turning on an axis. As it rotates, the rollers make contact with the outer diameter of the tubing. The rollers then press into the tubing, which must have some flexibility, to propel the media.

As one roller rotates away from the tube, another makes contact, continuing the constant motion of the contained fluid. Peristaltic pumps have a number of advantages over other pump designs. For instance, the fluid within the tube is not exposed to other pump components and only makes contact with the inside of the tube.

This prevents. The design also minimizes cleanup. When a tube has worn excessively, it is usually easy to remove and replace. Specialized peristaltic pumps are used in various medical applications.

The action of the pump is such that it does not damage blood vessels or blood cells. These devices assist blood flow in various surgical procedures and medical operations, such as open heart surgery, in which the beating heart must be stopped so the surgeon can properly place a new valve. What is a syringe and how does it work? A syringe is a pump consisting of a sliding plunger that fits tightly in a tube.

The plunger can be pulled and pushed inside the precise cylindrical tube, or barrel, letting the syringe draw in or expel a liquid or gas through an orifice at the open end of the tube. Pressure is used to operate a syringe. It is usually fitted with a hypodermic needle, nozzle, or tubing to help direct the flow into and out of the barrel. Plastic and disposable syringes are often used to administer medications. What is a hypodermic needle? A hypodermic hypo — under, dermic — the skin needle is a hollow needle commonly used with a syringe to inject substances into the body or extract fluids from it.

They may also be used to take liquid samples from the body, for example taking blood from a vein in venipuncture. Largebore hypodermic intervention is especially useful in treating catastrophic blood loss or shock.

A hypodermic needle also provides for rapid delivery of liquids. It is also used when the injected substance cannot be ingested orally, either because it would not be absorbed, as with insulin, or because it would harm the liver. Hypodermic needles also serve important roles in research requiring sterile conditions. The hypodermic needle significantly reduces contamination during inoculation of a sterile substrate in two ways.

What are electrical connectors? Just search on electrical connectors, scan the headlines, and you see these devices are available to do nearly everything. Some are small, or hold many connectors, work reliably after many connections and disconnections, and stay connected and disconnect easily when necessary. Some come with electronics for several functions, such as the prevention of short circuits. Plug arrangements must prevent misconnections, tolerate sterilizations, come with the right wires, be long and short, and lots more.

A few significant standards guide the designs of connectors: ISO helps maintain the good quality and design of medical connectors as well as other medical devices. This regulation helps ensure product safety and puts in place specific requirements for inspection, documentation, validation, and verification for medical connectors.

It is considered a standard requirement for medical devices, with its guidelines slowly becoming universal. IEC is a series of medical connector standards that require medical device companies to check the safety and risk potential that electrical connectors pose to patients and healthcare workers. To comply, companies must examine their products using an approved process and give every device a risk-management file. Manufacturers must be able to specify which connectors comply with technical requirements, and which satisfy the required performance characteristics.

Furthermore, any found with an unacceptable risk level must be eliminated. Even when they have electrically conductive surfaces, they are protected against contact with other live parts through the double insulation.

IEC standard describes requirements for detachable plug connections. The unit can be used on a bench top or is rack mountable. For each output option we offer a model with a RS and USB port and a model with no communication ports. The Interpower International Power Source can also be ordered for international use with a country-specific input power plug. We offer a 1-week U.

From 1 to 1, pieces or more, we have no minimum order requirements. Order Online! E-mail catalog interpower. Business Hours: 7 a. Central Time. You cannot control what you cannot measure, goes an old engineering saw. The measurement reference is accomplished by sensors. Each of these may have several methods of measurement. For temperature, pressure, and others, a sensing element experiences a change in electrical resistance in proportion to the change in the phenomenon, which produces a change in signal voltage often 0 to 5 volts, but PCB-mounted sensors are likely to have mV outputs that is calibrated to the changes in the measured phenomenon.

One position sensor locates the position of a magnetic field along a sensing tube. There are many other methods. A transducer, a type of sensor, is a device that converts one form of energy into another. Common units in medical apps include sensors to measure temperature, pressure, forces, liquid levels, and flow rates. These physical quantities are converted to electrical signals in either analog or digital form.

In motion control applications, transducers can refer to any one of a number of sensors, such as rotary or linear encoders, or resolvers for position feedback, such as tachometer for speed sensing, and even proximity switches to initiate or halt mechanical action.

If there is a trend in medical sensors, it is toward small and light-weight designs, and those that can sense small changes, and then function on millivolts. The need for sensors will increase as more healthcare devices are connected to the Internet and wearable technologies become more prevalent. Acceleration and vibration Acoustic and ultrasonic waves Chemicals and gases Electrical and magnetic fields Fluid flow rates Force, load, torque, and strain Humidity and moisture Leaks and fluid levels Velocity and displacement Temperature and pressure.

What are tubing connectors? Tubing connectors for medical applications come in an almost endless variety, but the recent thrust in their design is to prevent accidental connections. For instance, by one estimate a hospital room could have nine different fluids in use, making the possibility of a misconnection too high. That makes it important to have a simple and repeatable process for selecting the best connector. The process requires an analysis of the application to ensure connectors will be compatible with the physical, chemical, and biological environment, and be easy to use as well as help prevent misconnections.

The ISO series of standards will define non-interchangeable connectors that affect connector selections for a range of medical-device applications. Pressure drops across connectors and valves vary greatly by manufacturer. Furthermore, a mathematical model must be chosen which allows the probability to be calculated with which the hypothesis may be valid with regard to the data under study. Data have to be collected, prepared, evaluated, and calculated according to the model chosen.

The result obtained is represented by one or more digits, by a particular function, or the like. Its statistical evaluation leads to an acceptance or refusal of the hypothesis, and to a statement as to the significance of the results. The result must be linguistically interpreted, i. Now what does it mean, concretely, if one wants to construct a theory of language in the scientific understanding of this term? According to Altmann 5 , designing a theory of language must start as follows: When constructing a theory of language we proceed on the basic assumption that language is a self-regulating system all of whose entities and properties are brought into line with one another in some way or other.

From this perspective, general systems theory and synergetics provide a general framework for a science of language; the statistical formulation of the theoretical model thus can be regarded to represent a meta-linguistic interface to other branches of sciences. As a consequence, language is by no means un- derstood as a natural product in the 19th century understanding of this term; neither is it understood as something extraordinary within culture. Most rea- sonably, language lends itself to being seen as a specific cultural sign system.

Culture, in turn, offers itself to be interpreted in the framework of an evolu- tionary theory of cognition, or of evolutionary cultural semiotics, respectively. Culture thus is defined as the cognitive and semiotic device for the adaption of human beings to nature.

In this sense, culture is a continuation of nature on the one hand, and simultaneously a reflection of nature on the other — consequently, culture stands in an isologic relation to nature, and it can be studied as such.

Primarily, language is understood as a sign system serving as a vehicle of cognition and communication. Based on the further assumption that communicative processes are characterized by some kind of economy between the participants, language, regarded as an abstract sign system, is understood as the economic result of communicative processes.

Rather, we are concerned with a permanent process of mutual adaptation, and of a specific interrelation of partly contradictory forces at work, leading to a specific dynamics of an- tagonistic interest forces in communicative processes.

Communicative acts, as well as the sign system serving communication, thus represent something like a dynamic equilibrium. In principle, this view has been delineated by G.

Zipf as early as in the s and 40s cf. Zipf Today, Zipf is mostly known for his frequency studies, mainly on the word level; however, his ideas have been applied to many other levels of language too, and have been successfully transferred to other disciplines as well. It would be going too far to discuss the relevant ideas in detail here; still, the basic implications of this approach should be presented in order to show that the focus on word length chosen in this book is far from accidental. Word Length in a Synergetic Context Word length is, of course, only one linguistic trait of texts, among others.

In this sense, word length studies cannot be but a modest contribution to an overall science of language. However, a focus on the word is not accidental, and the linguistic unit of the word itself is far from trivial. Rather, word length is an important factor in a synergetic approach to lan- guage and text, and it is by no means an isolated linguistic phenomenon within the structure of language.

The question here cannot be, of course, in how far each of the units mentioned are equally adequate for lin- guistic models, in how far their definitions should be modified, or in how far there may be further levels, particularly with regard to specific text types such as poems, for example, where verses and stanzas may be more suitable units. At closer inspection cf. Table 1. Consequently, on each of these levels, the re-occurrence of units results in particular frequencies, which may be modelled with recourse to specific frequency distribution models.

To give but one example, the fa- mous Zipf-Mandelbrot distribution has become a generally accepted model for word frequencies. Models for letter and phoneme frequencies have recently been discussed in detail. It turns out that the Zipf-Mandelbrot distribution is no adequate model, on this linguistic level cf. Moreover, the units of all levels are characterized by length; and again, the length of the units on one level is directly interrelated with those of the neigh- boring levels, and, probably, indirectly with those of all others.

Altmann Finally, systematic dependencies cannot only be observed on the level of length; rather, each of the length categories displays regularities in its own right.

Thus, particular frequency length distributions may be modelled on all levels distinguished. Yet, many a problem still begs a solution; in fact, even many a question remains to be asked, at least in a systematic way.

Thus, the descriptive apparatus has been excellently devel- oped by structuralist linguistics; yet, structuralism has never made the decisive next step, and has never asked the crucial question as to explanatory models. Also, the methodological apparatus for hypothesis testing has been elaborated, along with the formation of a great amount of valuable hypotheses. Still, much work remains to be done. From another perspective, this work will throw us back to the very basics of empirical study.

Last but not least, the quality of scientific research depends on the quality of the questions asked, and any modification of the question, or of the basic definitions, will lead to different results. As long as we do not know, for example, what a word is, i. And how, or in how far, do the results change — and if so, do they systematically change? These questions have never been systematically studied, and it is a problem sui generis, to ask for regularities such as frequency distributions on each of the levels mentioned.

But ultimately, these questions concern only the first degree of un- certainty, involving the qualitative decision as to the measuring units: given, we clearly distinguish these factors, and study them systematically, the next questions concern the quality of our data material: will the results be the same, and how, or in how far, will they systematically?

At this point, the im- portant distinction of types and tokens comes into play, and again the question must be, how, or in how far, the results depend upon a decision as to this point.

Thus far, only language-intrinsic factors have been named, which possibly influence word length; and this enumeration is not even complete; other factors as the phoneme inventory size, the position in the sentence, the existence of suprasegmentals, etc. And, finally, word length does of course not only depend on language-intrinsic factors, according to the synergetic schema represented in Table 1.

More questions than answers, it seems. And this may well be the case. Asking a question is a linguistic process; asking a scientific question, is a also linguistic process, — and a scientific process at the same time. The crucial point, thus, is that if one wants to arrive at a science of language, one must ask questions in such a way that they can be answered in the language of science.

Koch ed. Faust; R. Harweg; W. Lehfeldt; G. Wienold eds. Altmann, Gabriel; Schwibbe, Michael H. Hildesheim etc. Bunge, Mario Scientific Research I. The Search for Systems. Berlin etc. Collinge, Neville E. Stuttgart, Koch, Walter A. Evolutionary Cultural Semiotics. Struktur und Dynamik der Lexik.

Rickert, Heinrich Kulturwissenschaft und Naturwissenschaft. Smith, Neilson Y. Snow, Charles P. Cambridge, Woodbury, NY. Windelband, Wilhelm Geschichte und Naturwissenschaft. Zipf, George K. Cambridge, Mass. An introduction to human ecology. Cam- bridge, Mass. Peter Grzybek ed. Dordrecht: Springer, , pp.

Historical roots The study of word length has an almost year long history: it was on August 18, , when Augustus de Morgan, the well-known English mathematician and logician — , in a letter to a friend of his, brought forth the idea of studying word length as an indicator of individual style, and as a possible factor in determining authorship.

Specifically, de Morgan concentrated on the number of letters per word and suspected that the average length of words in differ- ent Epistles by St. Paul might shed some light on the question of authorship; generalizing his ideas, he assumed that the average word lengths in two texts, written by one and the same author, though on different subjects, should be more similar to each other than in two texts written by two different individuals on one and the same subject cf.

Lord Thackerey, and John Stuart Mill. Figure 2. Still, Mendenhall concentrated on solely on word length, as he did in his follow-up study of , when he continued his earlier line of research, extend- ing it also to include selected passages from French, German, Italian, Latin, and Spanish texts.

In fact, what Mendenhall basically did, was what would nowadays rather be called a frequency analysis, or frequency distribution analysis. He personally was mainly attracted to the frequency distribution technique by its resemblance to spectroscopic analysis. Particularly as to the question of au- thorship, Williams emphasized that before discussing the possible significance of the Shakespeare—Bacon and the Shakespeare—Marlowe contro- versies, it is important to ask whether any differences, other than authorship, were involved in the calculations.

Grzybek et al. Thus, the least one would expect would be to count the number of sounds, or phonemes, per word; as a matter of fact, it would seem much more reasonable to measure word length in more immediate constituents of the word, such as syllables, or morphemes. Yet, even today, there are no reliable systematic studies on the influence of the measuring unit chosen, nor on possible interrelations between them and if they exist, they are likely to be extremely language- specific.

More often than not, the reason for this procedure is based on the statistical assumption that, from a well-defined sample, one can, with an equally well-defined degree of probability, make reliable inferences about some totality, usually termed population.

Now, for some linguistic questions, samples of words may be homogeneous — for example, this seems to be the case with letter frequencies cf. The very same, of course, has to be said about corpus analyses, since a corpus, from this point of view, is nothing but a quasi text.

However, much of this criticism must then be directed towards contemporary research, too. Particularly the last point mentioned above, leads to the next period in the history of word length studies.

As can be seen, no attempt was made by Mendenhall to find a formal mathe- matical model, which might be able to describe or rather, theoretically model the frequency distribution.

As a consequence, no objective comparison between empirical and theoretical distributions has been possible. In this respect, the work of a number of researchers whose work has only recently and, in fact, only partially been appreciated adequately, is of utmost im- portance.

These scholars have proposed particular frequency distribution mod- els, on the one hand, and they have developed methods to test the goodness of the results obtained. Initially, most scholars have implicitly or explicitly shared the assumption that there might be one overall model which is able to represent a general theory of word length; more recently, ideas have been devel- oped assuming that there might rather be some kind of general organizational principle, on the basis of which various specific models may be derived.

The present treatment concentrates on the rise and development of such models. It goes without saying that without empirical data, such a discussion would be as useless as the development of theoretical models. Consequently, the following presentation, in addition to discussing relevant theoretical models, will also try to present the results of empirical research.

Studies of merely empirical orientation, without any attempt to arrive at some generalization, will not be mentioned, however — this deliberate concentration on theory may be an important explanation as to why some quite important studies of empirical orientation will be absent from the following discussion. The first models were discussed as early as in the late s.

Research then concentrated on two models: the Poisson distribution, and the geometric dis- tribution, on the other. Later, from the mids onwards, in particular the Poisson distribution was submitted to a number of modifications and gener- alizations, and this shall be discussed in detail below.

The first model to be discussed at some length, here, is the geometric distribution which was sug- gested to be an adequate model by Elderton in Elderton — , who had published a book on Frequency-Curves and Correlation some decades before London , studied the frequency of word lengths in passages from English writers, among them Gray, Macaulay, Shakespeare, and others.

As opposed to Mendenhall, Elderton measured word length in the number of syllables, not letters, per word. His assumption was that the frequency distributions might follow the geometric distribution. It seems reasonable to take a closer look at this suggestion, since, histori- cally speaking, this was the first attempt ever made to arrive at a mathematical description of a word length frequency distribution.

Where are zero-syllable words, i. Table 2. Gray Elderton Number of Frequency of syllables x-syllable words xi fi pi 1 0. Therefore, formula 2. The theoretical data, obtained by fitting the geometric distribution 2 to the empirical data from Table 2. Thus, with d. Therefore, the larger a sample, the more likely the deviations tend to be statistically significant.

What is problematic about his approach is not so much that his attempt was only partly successful for some English texts; rather, it is the fact that the geometrical distribution is adequate to describe monotonously decreasing distributions only. Analyzing randomly chosen lexical material from a Lithuanian dictionary, he found differences as to the distribution of root words and words with affixes. As an empirical test shows, the geometric distribution indeed turns out to be a good model.

In order to test his hypothesis, he gives, by way of an example, the relative frequencies of a list of dictionary words taken from a Lithuanian-French dic- tionary, represented in Table 2. The whole sample is thus arbitrarily divided into two portions, assuming that at a particular point of the data, there is a rupture in the material. With regard to the data presented in Table 2. The approach as a whole thus implies that word length frequency would not be explained as an organic process, regulated by one overall mechanism, but as being organized by two different, overlapping mechanisms.

In fact, this is a major theoretical problem: Given one accepts the suggested separation of different word types — i. Yet, this raises the question whether a unique, common model might not be able to model the Lithuanian data from Table 2. In fact, as the re-analysis shows, there is such a model which may very well be fitted to the data; we are concerned, here, with the Conway-Maxwell-Poisson cf.

What is more important, how- ever, is the fact that, in the case of the Conway-Maxwell-Poisson distribution, no separate treatment of two more or less arbitrarily divided parts of the whole sample is necessary, so that in this case, the generation of word length follows one common mechanism. His linguistic interests, to our knowledge, mainly concen- trated on the process of language development. Since the support of 2. By way of an example, his approach will be demonstrated here, with reference to three texts.

These data shall be additionally analyzed here because they are a good example for showing that word length frequencies do not necessarily imply a monotonously decreasing profile cf. The absolute frequencies fi , as presented by Cebanov , as well as the corresponding relative frequencies pi , are represented in Table 2. Let us demonstrate this with reference to the data from Parzival in Table 2.

Well 5 As compared to the calculations above, the theoretical frequencies slightly differ, due to rounding effects. In Figure 2. As opposed to the approaches thus far discussed, these authors did not try to find a discrete distribution model; rather, they worked with continuous models, mainly the so-called lognormal model. Herdan was not the first to promote this idea with regard to language.

Before him, Williams , had applied it to the study of sentence length fre- quencies, arguing in favor of the notion that the frequency with which sentences of a particular length occur, are lognormally distributed.

This assumption was brought forth, based on the observation that sentence length or word length frequencies do not seem to follow a normal distribution; hence, the idea of lognormality was promoted.

Later, the idea of word length frequencies being lognormally distributed was only rarely picked up, such as for example by Rus- sian scholar Piotrovskij and colleagues Piotrovskij et al. Generally speaking, the theoretical background of this assumption can be characterized as follows: the frequency distribution of linguistic units as of other units occurring in nature and culture often tends to display a right-sided asymmetry, i.

One of the theoretical reasons for this can be seen in the fact that the variable in question cannot go beyond or remain below a particular limit; since it is thus characterized by a one-sided limitation in variation, the distribution cannot be adequately approximated by the normal distribution.

In other words: the left part of the distribution is stretched, and at the same time, the right part is compressed. Given the probability density function for the normal distribution as in 2. These two studies contain data on word length frequencies, the former 78, words of written English, the latter 76, words of spoken English. Thus, Herdan had the opportunity to do comparative analyses of word length frequencies measured in letters and phonemes.

In order to test his hypothesis as to the lognormality of the frequency distribution, Herdan confined himself to graphical techniques only. The most widely applied method in his time was the use of probability grids, with a logarithmically divided abscissa x-axis and the cumulative frequencies on the ordinate y- axis. If the resulting graph showed a more or less straight line, one regarded a lognormal distribution to be proven. As can be seen from Figure 2.

The latter had analyzed several French samples, among them the three picked up by Herdan in Figure 2. The corresponding graph is reproduced in Figure 2. In his book, he offered theoretical arguments for the lognormal distribution to be an adequate model Herdan However, Herdan did not do any comparative analyses as to the efficiency of the normal or the lognormal distribution, neither graphically nor statistically.

Therefore, both procedures shall be presented here, by way of a re-analysis of the original data. As far as graphical procedures are concerned, probability grids have been replaced by so-called P-P plots, today, which also show the cumulative pro- portions of a given variable and should result in a linear rise in case of normal distribution.

By way of an example, Figure 2. It can clearly be seen that there are quite some deviations for the lognor- mal distribution cf.

What is even more important, however, is the fact that the deviations are clearly less expressed for the normal distribu- tion cf. Although this can, in fact, be shown for all three data samples mentioned above, we will concentrate on a statistical analysis of these observations.

Furthermore, differences between normal and lognormal are minimal; in case of Manon Lescaut, the lognormal distribution is even worse than the normal distribution. The same holds true, by the way, for the above-mentioned data presented by Piotrovskij et al.

As a re-analysis of the data shows, this claim may not be upheld, however cf. However, as can be seen the deviation from the lognormal distribution is highly significant as well, and, strictly speaking, even greater compared to the normal distribution. With regard to this negative finding, one may add the result of a further re-analysis, saying that in case of all three data samples discussed by Herdan, the binomial distribution can very well be fitted to the empirical data, with 0.

Incidently, Michel arrived at the very same conclusion, in an exten- sive study on Old and New Bulgarian, as well as Old and new Greek material. He tested the adequacy of the lognormal distribution for the word length fre- quencies of the above-mentioned material on two different premises, basing his calculation of word length both on the number of letters per word, and on the number of syllables per word.

Additionally, and this is even more important in the given context, one must state that there are also major theoretical problems which arise in the context of the log- normal distribution as a possible model for word length frequencies: a.

With this in mind, let us return to discrete models. The next historical step in the history of word length studies were the important theoretical and empirical analyses by Wilhelm Fucks, a German physician, whose theoretical models turned out to be of utmost importance in the s and s.

The Fucks Generalized Poisson Distribution 5. Cebanov in the late s. Interestingly enough, some years later the very same model — i. Piotrowski et al. Furthermore, Fucks, in a number of studies, developed many important ideas on the general functioning not only of language, but of other human sign systems, too. In its most general form, this weighting generalization results in the following formula 2.

For 2. As can be seen from equation 2. As was already mentioned above, the only model which met general ac- ceptance was the 1-displaced Poisson distribution. It is no wonder, then, that the generalized model has practically not been discussed. Fucks Thus, his application of the 1-displaced Poisson distribution included studies on 1 the individual style of single authors, as well as on 2 texts from different authors either 2. As an example of the study of individual texts, Figure 2.

As can be seen from the dotted line in Figure 2. As to a comparison of two German authors, Rilke and Goethe, on the one hand, and two Latin authors, Sallust and Caesar, on the other, Figure 2. Again, the fitting of the 1-displaced Poisson distribution seems to be convincing. Yet, in re-analyzing his works, there remains at least one major problem: Fucks gives many characteristics of the specific distributions, starting from mean values and standard deviations up to the central moments, entropy etc.

Yet, there are hardly ever any raw data given in his texts, a fact which makes it impossible to check the results at which he arrived. Thus, one is forced to believe in the goodness of his fittings on the basis of his graphical impressions, only; and this drawback is further enhanced by the fact that there are no procedures which are applied to test the goodness of his fitting the 1-displaced Poisson distribution. There is only one instance where Fucks presents at least the relative, though not the absolute frequencies of particular distributions in detail.

Fucks a: 85ff. The relative frequencies are reproduced in Table 2. We will come back to these data throughout the following discussion, using them as exemplifying material. Being well aware of the fact that for each of the languages we are concerned with mixed data, we can ignore this fact, and see the data as a representation of a maximally broad spectrum of different empirical distributions which may be subjected to empirical testing.

As was mentioned above cf. Remembering that fitting is considered to be good in case of 0. Still, Fucks and many followers of his pursued the idea of the 1-displaced Poisson distribution as the most adequate model for word length frequencies. Thus, one arrives at the curve in Figure 2. Fucks a: As can be seen with Fucks a: 88, f. And again, it would have been easy to run such a statistical test, calculating the co- efficient of determination R2 in order to test the adequacy of the theoretical curve obtained.

Let us shortly discuss this procedure: in a nonlinear regression model, R 2 represents that part of the variance of the variable y, which can be explained by variable x.

There are quite a number of more or less divergent formulae to calculate R2 cf. Grotjahn , which result in partly significant differences. Usually, the following formula 2. Thus, for each empirical x i , we need both yi which can be obtained by the empirical values yi and the theoretical values b formula 2. Still, there remains a major theoretical problem with the specific method chosen by Fucks in trying to prove the adequacy of the 1-displaced Poisson distribution: this problem is related to the method itself, i.

Taking a second look at formula 2. To summarize, one has thus to draw an important conclusion: Due to the fact that Fucks did not apply any suitable statistics to test the goodness of fit for the 1-displaced Poisson distribution, he could not come to the point of explicitly stating that this model may be adequate in some cases, but is not acceptable as a general standard model.

Most of these subsequent studies concentrated on the 1-displaced Poisson distribution, as suggested by Fucks. In fact, work on the Poisson distribution is by no means a matter of the past. Discussing and testing various distribution models, Rothschild did not find any one of the models he tested to be adequate.

As was said above, Michel first found the lognormal distribution to be a completely inadequate model. He then tested the 1-displaced Poisson distribution and obtained negative results as well: although fitting the Poisson distribution led to better results as compared to the lognormal distribution, word length in his data turned out not to be Poisson distributed, either Michel f.

Finally, Grotjahn whose work will be discussed in more detail below cf. In doing so, let us first direct our attention to the 2-parameter model suggested by him, and then to his 3-parameter model. In a similar way, two related 2-parameter distributions can be derived from the general model 2.

It is exactly the latter distribution 2. Fucks has not systematically studied its relevance; still, it might be tempting to see what kind of results are yielded by this distribution for the data already analyzed above cf. As in the case of the 1-displaced Poisson distribution, one has thus to ac- knowledge that the Fucks 2-parameter 1-displaced Dacey-Poisson distribution is an adequate theoretical model only for a specific type of empirical distribu- tions.

This leads to the question whether the Fucks 3-parameter distribution is more adequate as an overall model. It would lead too far, here, to go into details, as far as their derivation is concerned. Consequently, three solutions are obtained, not all of which must necessarily be real solutions. With this in mind, let us once again analyze the data of Table 2. The results obtained can be seen in Table 2. It can clearly be seen that in some cases, quite reasonably, the results for the 3-parameter model are better, as compared to those of the two models discussed above.

From the results represented in Table 2. These violations can be of two kinds: a. However, some of the problems met might be related to the specific way of estimating the parameters suggested by him, and this might be the reason why other authors following him tried to find alternative ways. Cercvadze, G. As opposed to most of his German papers, Fucks had discussed his generalization at some length in this English synopsis of his work, and this is likely to be the reason why his approach received much more attention among Russian-speaking scholars.

We need not go into details, here, as far as the derivation of the Fucks dis- tribution and its generating function is concerned cf. Unfortunately, Piotrovskij et al. Based on the standard Poisson distribution, as represented in 2. Based on these assumptions, the following special cases are obtained for 2. These analyses comprised nine Polish literary texts, or segments of them, and the results of these analyses indeed proved their approach to be successful.

For the sake of comparison, Table 2. A closer look at these data shows that the Polish text samples are relatively homogeneous: for all texts, the dispersion quotient is in the interval 0. The authors analyzed Croatian data from two corpora, each consisting of several literary works and a number of news- paper articles.

The data of one of the two samples are represented in Table 2. Frequency observed Poisson 0 1 2 3 4 5 6 7 8 Syllables per word Figure 2. Rather, it is of methodological interest to see how the authors dealt with the data. Guided by the conclusion supported by the graphical representation of Figure 2. Still, there remain at least two major theoretical problems: 1.

No interpretation is given as to why the weighting modification is necessary: is this a matter of the specific data structure, is this specific for Croatian language products?

As the re-analyses presented in the preceding chap- ters have shown, neither the standard Poisson distribution nor any of its straight forward modifications can be considered to be an adequate model.

Grotjahn, in his attempt, opened the way for new perspectives: he not only showed that the Poisson model per se might not be an adequate model; fur- thermore, he initiated a discussion concentrating on the question whether one overall model could be sufficient when dealing with word length frequencies of different origin.

As a starting point, Grotjahn analyzed seven letters by Goethe, written in , and tested in how far the 1-displaced Poisson distribution would prove to be an adequate model.

As was pointed out above cf. However, of the concrete data analyzed by Grotjahn, only some satisfied this condition; others clearly did not, the value of d ranging from 1. In a way, this conclusion paved the way for a new line of research. After decades of concentration on the Poisson distribution, Grotjahn was able to prove that this model alone cannot be adequate for a general theory of word length distribution. On the basis of this insight, Grotjahn further elaborated his ruminations.

Although every single word thus may well follow a Poisson distribution, this assumption does not necessarily imply the premise that the probability is one and the same for all words; rather, it depends on factors such as linguistic context, theme, etc. Grotjahn 56ff. Thus, the so-called negative binomial distribution 2. Therefore, as Grotjahn 71f.

With his approach, Grotjahn thus additionally succeeded in integrating earlier research, both on the geometric and the Poisson distributions, which had failed to be adequate as an overall valid model.

The data are reproduced in Table 2. Poisson d. The results are graphically repre- sented in Figure 2. History and Methodology of Word Length Studies 65 f x neg. Poisson 0 1 2 3 4 5 6 7 8 9 Figure 2. Still, it is tempting to see in how far the negative binomial distribution is able to model the data of nine languages, given by Fucks cf.

Their discussion is of unchanged importance, still today, since many more recent studies in this field do not seem to pay sufficient attention to the ideas expressed almost a decade ago. Before discussing these important reflections, one more model should be discussed, however, to which attention has recently been directed by Kromer a,b,c; In this case, we are concerned with the Poisson-uniform distribution, also called Poisson-rectangular distribution cf. In his approach, Kromer a derived the Poisson-uniform distribution along a different theoretical way, which need not be discussed here in detail.

With regard to formula 2. It would be too much, here, to completely derive the two relevant equa- tions anew. It may suffice therefore to say that the first equation can easily be derived from 2. Best, in turn, had argued in favor of the negative binomial distribution discussed above, as an adequate model. The results obtained for these data need not be presented here, since they can easily be taken from the table given by Kromer a: These data have been repeatedly analyzed above, among others with regard to the negative binomial distribution cf.

Using the method of moments, it turns out that in four of the nine cases Esperanto, Arabic, Latin, and Turkish , no acceptable solutions are obtained.

Now, what is the reason for no satisfying results being obtained, according to the method of moments? Empirically, this is proven by the results represented in Table 2. History and Methodology of Word Length Studies 71 Poisson-uniform distribution suggested by Kromer personal communication shall be demonstrated here; it is relevant for those cases when parameter a con- verges with parameter b in equation 2.

Parameter I, according to him, expresses something like the specifics of a given language i. Unfortunately, most of the above-mentioned papers Kromer b,c; have the status of abstracts, rather than of complete papers; as a consequence, only scarce empirical data are presented which might prove the claims brought forth on a broader empirical basis. If his assumption should bear closer examination on a broader empirical basis, this might as well explain why we are concerned here with a mixture of two distributions.

However, one must ask the question, why it is only the rectangular distribution which comes into play here, as one of two components. Strangely enough, it is just the Poisson-uniform distribution, which converges to almost no other distribution, not even to the Poisson distribution, as can be seen above for details, cf.

This discussion was initiated by Grotjahn and Altmann as early as in , and it seems impor- tant to call to mind the most important arguments brought forth some ten years ago. Yet, only recently systematic studies have been un- dertaken to solve just the methodological problems by way of empirical studies. Nevertheless, most of the ideas discussed — Grotjahn and Alt- mann combined them in six groups of practical and theoretical problems — are of unchanged importance for contemporary word length studies, which makes it reasonable to summarize at least the most important points, and comment on them from a contemporary point of view.

The problem of the unit of measurement. In other words: There can be no a priori decision as to what a word is, or in what units word length can be measured. Meanwhile, in contemporary theories of science, linguistics is no exception to the rule: there is hardly any science which would not acknowledge, to one degree or another, that it has to define its object, first, and that constructive processes are at work in doing so.

The relevant thing here is that measuring is made possible, as an important thing in the construction of theory. What has not yet been studied is whether there are particular dependencies between the results obtained on the basis of different measurement units; it goes without saying that, if they exist, they are highly likely to be language- specific.

Also, it should be noted that this problem does not only concern the unit of measurement, but also the object under study: the word. It is not even the problem of compound words, abbreviation and acronyms, or numbers and digits, which comes into play here, or the distinction between word forms and lexemes lemmas — rather it is the decision whether a word is to be defined on a graphemic, orthographic-graphemic, or phonological level. The population problem. Again, as to these questions, there are hardly any systematic studies which would aim at a comparison of results obtained on an empirical basis.

However, there are some dozens of different types of letters, which can be proven to follow different rules, and which even more clearly differ from other text types. The goodness-of-fit problem. Rather, the question is, what is a small text, and where does a large text start? History and Methodology of Word Length Studies 75 d. The problem of the interrelationship of linguistic properties. What they have in mind are in- tralinguistic factors which concern the synergetic organization of language, and thus the interrelationship between word length factors such as size of the dictionary, or the phoneme inventory of the given language, word frequency, or sentence length in a given text to name but a few examples.

As soon as the interest shifts from language, as a more or less abstract system, to the object of some real, fictitious, imagined, or even virtual communicative act, between some producer and some recipient, we are not concerned with language, any more, but with text.

Consequently, there are more factors to be taken into account forming the boundary conditions, factors such as author- specific, or genre-dependent conditions.

Ultimately, we are on the borderline here, between quantitative linguistics and quantitative text analysis, and the additional factors are, indeed, more language-related than intralinguistic in the strict sense of the word. It should be mentioned, however, that very little is known about such factors, and systematic work on this problem has only just begun. The modelling problem. As can be seen, the aim may be different with regard to the particular research object, and it may change from case to case; what is of crucial relevance, then, is rather the question of interpretability and explanation of data and their theoretical modelling.

The problem of explanation. Consequently, in order to obtain an explanation of the nature of word length, one must discover the mechanism generating it, hereby taking into account the necessary boundary conditions.

Thus far, we cannot directly concentrate on the study of particular boundary conditions, since we do not know enough about the general system mechanism at work. Consequently, contemporary research involves three different kinds of orientation: first, we have many bottom-up oriented, partly in the form of ad-hoc solutions for particular problems, partly in the form of inductive research; second, we have top-down oriented, deductive research, aiming at the formulation of general laws and models; and finally, we have much exploratory work, which may be called abductive by nature, since it is characterized by constant hypothesis testing, possibly resulting in a modification of higher-level hypotheses.

In this framework, it is not necessary to know the probabilities of all individual frequency classes; rather, it is sufficient to know the relative difference between two neighboring classes, e.

Ultimately, this line of research has in fact provided the most important research impulses in the s, which shall be discussed in detail below. In their search for relevant regularities in the organization of word length, Wimmer et al. Wimmer et al. This model was already discussed above, in its 1-displaced form 2. It has also been found to be an adequate model for word length frequencies from a Slovenian frequency dictionary Grzybek After corresponding re-parametrizations, these modifications result in well-known distribution models.

In , Wimmer et al. The set of word length classes is organized as a whole, i. Now, different distributions may be inserted for j. Thus, inserting the Borel distribution cf. The parameters a and b of the GPD are independent of each other; there are a number of theoretical restrictions for them, which need not be discussed here in detail cf.

Irrespective of these restrictions, already Wimmer et al. These observations are supported by recent studies in which Stadlober analyzed this distribution in detail and tested its adequacy for linguistic data. Stadlober As can be seen, the results are good or even excellent in all cases; in fact, as opposed to all other distributions discussed above, the Consul-Jain GPD is able to model all data samples given by Fucks.

It can also be seen from Table 2. In this respect, i. As to this problem, it seems however important to state that this is not a problem specifically related to the GPD; rather, any mixture of distributions will cause the very same problems.

In this respect, it is important that other distributions which imply no mixtures can also be derived from 2. It would go beyond the frame of the present article to discuss the various extensions and modifications in detail here. As a result, there seems to be increasing reason to assume that there is in- deed no unique overall distribution which might cover all linguistic phenom- ena; rather, different distributions may be adequate with regard to the material studied.

This assumption has been corroborated by a lot of empirical work on word length studies from the second half of the s onwards. Best More often than not, the relevant analyses have been made with specialized software, usually the Altmann Fitter.

This is an interactive computer pro- gram for fitting theoretical univariate discrete probability functions to empirical frequency distributions; fitting starts with the common point estimates and is optimized by way of iterative procedures. There can be no doubt about the merits of such a program. Now, the door is open for inductive research, too, and the danger of arriving at ad-hoc solutions is more virulent than ever before.

What is important, therefore, at present, is an abductive approach which, on the one hand, has theory-driven hypotheses at its background, but which is open for empirical findings which might make it necessary to modify the theoretical assumptions. In addition to the C values of the discrepancy coefficient, the values for parameters a and b as a result of the fitting are given. As can be seen, fitting results are really good in all cases.

As to the data analyzed, at least, the hyper-Poisson distribution should be taken into account as an alternative model, in addition to the GDP, suggested by Stadlober Comparing these two models, a great advantage of the GPD is the fact that its reference value can be very easily calculated — this is not so convenient in the case of the hyper-Poisson distribution. On the other hand, the generation of the hyper-Poisson distribution does not involve any secondary distribution to come into play; rather, it can be directly derived from equation 2.

In its 1-displaced form, equation 2. To summarize, we can thus state that the synergetic approach as developed by Wimmer et al. Generally speaking, the authors understand their contribution to be a logical extension of their synergetic approach, unifying previous assumptions and empirical findings.

The individual hypotheses belonging to the proposed system have been set up earlier; they are well-known from empirical research of the last decades, and they are partly derived from different approaches.

Specifically, Wimmer et al. History and Methodology of Word Length Studies 85 it is confined to the first four terms of formula 2. Many distributions can be derived from 2. It can thus be said that the general theoretical assumptions implied in the synergetic approach has experienced strong empirical support. One may object that this is only one of possible alternative models, only one theory among others.

However, thus far, we do not have any other, which is as theoretically sound, and as empirically supported, as the one presented. On the other hand, hardly any systematic studies have been undertaken to empirically study pos- sible influencing factors, neither as to the data basis in general i. Ultimately, the question, what may influence word length frequencies, may be a bottomless pit — after all, any text production is an historically unique event, the boundary conditions of which may never be reproduced, at least not completely.

Still, the question remains open if particular factors may be detected, the relevance of which for the distribution of word length frequencies may be proven. This point definitely goes beyond a historical survey of word length studies; rather, it directs our attention to research desires, as a result of the methodolog- ical discussion above. A, ; — Best, Karl-Heinz ed. Brainerd, Barron Weighing evidence in language and literature: A statistical approach. Chebanow Chebanow, S. Dewey, G. Cambridge; Mass.

Elderton, William P. London, Fucks, Wilhelm Nach allen Regeln der Kunst. Leningrad, Nauka: — Dordrecht, NL. Grzybek, Peter ed. Ljubljana etc.

The Impact of Word Length. Kromer, Victor V. Materialy konferencii. Ma- terialy konferencii. Markov, Andrej A. Mendenhall, Thomas C. Studien zum 1. Internationalen Bulgaristikkongress Sofia Piotrovskij, Rajmond G. Williams, Carrington B. Wimmer, Gejza; Altmann, Gabriel Thesaurus of univariate discrete probability distributions. Zerzwadse, G. In: Grundlagenstudien aus Kybernetik und Geisteswissenschaft 4, — The idea is derived from the Fitts—Garner controversy in mathematical psychology cf.

Fitts et al. Obviously, the problem is quite old but has not penetrated into linguistics as yet. A word in a text can be thought of as a realization of a number of different alternative possibilities, see Fig. They can even be understood in different ways, e. What is neglected when correlating the lengths and the frequencies of words in real texts is the fact that for the text producer there is not at all free choice of all existing words at every moment. Trying to fill in the blank is a model for determining the uncertainty of the missing word.

It must be noted that SIC or HIC are associated not only with words but also with whole phrases or clauses, so that they represent rather polystratic structures and sequences. The present approach is the first approximation at the word level. Preparation In order to illustrate the variables which will be treated later on, let us first define some quantities. The cardinality of the set X will be symbolized as X.

P the set of positions in a text, whatever the counting unit. The elements of this set are tokens tijk , i. If the type and its token are known, the indices i and j can be left out.

The elements of this set, aij , are not necessarily synonyms but in the given context they are admissible alternatives of the given token. The index k can be omitted Aij the number of elements in the set Aij , i. This entity can be called tokeme. By defining Mij , we are able to distinguish between tokens of the same type but with different alternatives and different number ai — so they are different tokemes.

Example Using Table 9 cf. The text is reproduced word for word in the second column of Table 9 p. The length is measured in terms of the number of syllables of the word. Thus, e. We can define it for types too: then it is the mean of all LLs of all tokens of this type in the text.

LL is usually a positive real number. The errors compensate each other in the long run, so the distribution of L equals that of LL. It can be ascertained for any text. We can set up the hypothesis that Hypothesis 1 The longer the token, the longer the tokeme at the given position. This hypothesis can be tested in different ways. As an empirical consequence of hypothesis 1 it can be expected that the distribution of L and LL is approximately equal.

A token of length L has alternatives which are on average the same length, i. Since LL is a positive real number it is an average we divide the range of lengths in the text in continuous intervals and ascertain the number of cases the frequency in the particular intervals. This can easily be made using the third and the sixth column of Table 9 p. The result is presented in Table 3. It can easily be shown that the frequencies differ non-significantly.

Since the distributions are equal, they must abide by the same theoretical distribution. Using the well corroborated theory of word length cf. Wim- mer et al. As a matter of fact, for the distribution of LL we take the middles of the intervals as variable. It would, perhaps, be more correct to use for both data the continuous equivalent of the geometric distribution, namely the exponential distribution — however, again not quite correct.

Thus we adhere to discreteness without loss of validity. The result of fitting the geometric distribution to the data from Table 3. Length range in tokemes In each tokeme the lengths of words local latent lengths are distributed them- selves in a special way.

It is not fertile to study them individually since the majority of them is deterministic i. It is more prolific to consider the ranges of latent lengths for the whole text. For this phenomenon we set up the hypothesis Hypothesis 2 The range of latent lengths within the tokemes is geometric-Poisson.

Since the latent length distribution LLx is geometric and each LLx is al- most identical on average with that of Lx the alternatives tend to keep the length of the token , the range of the latent lengths in the tokeme is very restricted. The deviations seem to be distributed at random, i. Evidently, the fitting is very good and corroborates in addition hypothesis 1, too. Thus latent length is a kind of latent mechanism controlling the token length at the given position.

Latent length is not directly measurable, it is an invisible result of the complex flow of information. Nevertheless, it can be made visible — as we tried to do above — or it can be approximately deduced on the basis of token lengths. Information Content of Words in Texts 99 Table 3. Stable latent length Consider the deviations of the individual token lengths from those of the re- spective tokeme lengths as shown in Table 9 p. This encourages us to set up the hypothesis that Hypothesis 3 There is no tendency to choose the smallest possible alternative at the given position in text.

The hypothesis can easily be tested. SIC of the text Above, we defined SIC of a type as the dual logarithm of the mean size of all tokeme sizes of the given type, as shown in formula 3. Two possibilities can be proposed. We shall use here 3. For the given text it can be computed directly using the fifth column of Table 9 p.

We suppose that it is the smaller the more formal the text. We can build about it a confidence interval. Here the tokeme sizes build a sequence of a 1, 16, 3, 2, 1, 8, 2, 1,. Taking the dual logarithms we obtain a new sequence b 0, 4, 1. In order to control the information flow and at the same time to allow licentia poetica, zeros and non-zeroes must display some pattern which is characteristic of different text types.

Thus we obtain the two state sequence c 0, 1, 1, 1, 0, 1, 1, 0,. We begin with the examination of runs of 0 and 1 and set up the hypothesis that Hypothesis 4 The building of text blocks with zero uncertainty 0 and those with selection possibilities 1 is random i.

In practice it means that the runs of zeroes and ones are distributed at random. In our text see Table 9 , p. Another possibility is to consider sequence c as a two-state Markov chain or sequences a and b as multi-state Markov chains. In the first approx- imation we consider case c as a dynamical system and compute the transition matrix between zeroes and ones. Taking the powers of the above matrix we can easily see that the probabilities are stable to four decimal places with P 4 yielding a matrix with equal rows [0.

Since P n represents the n-step transition prob- ability matrix, the exponent n is also a characteristic of the text. Alternatives, length and frequency Since SIC has not been imbedded in the network of synergetic linguistics as yet, it is quite natural to ask whether it is somehow associated with basic language properties such as length and frequency. In the present paper all other properties e. The data for testing can easily be prepared using Table 9 p.

Below we show merely lengths 4 and 5 because the full Table is very extensive cf. Table 3. This results in Table 3. In such cases they must be taken into account explicitly. In our case this leads to partial differential equations. Let us assume that length has a constant effect, i. Fitting this curve to the data in Table 3. This is, of course, merely the first approximation using data smoothing because the text was rather a short one. Interpretation and outlook Looking at Tables 3.

But we recognize that the influence of frequency is considerably weaker than that of length. If we regard 3.

The direction of this influence is even more astonishing: with increasing length the number of alternatives is increasing too, longer words are more often freely chosen, while one perhaps would expect a preference for choosing shorter words.

Since the e-function plays an important role in psychology, for example in cognitive tasks like decision making, we suppose that word length is a variable which is connected with some basic cognitive psychological processes. Andersen, S. Attneave, F. New York. Berlyne, D. Coombs, C. Englewood Cliffs, N.