Rack-and-pinion mechanisms convert between linear and rotary motion. Mapping is determined by the rack’s linear pitch (i.e., tooth-to-tooth spacing) compared to the number of teeth on the pinion. Backlash is inevitable.

Lead-screws convert rotary motion to linear motion via the screw principle. Certain low-friction types (e.g., ball-screws) are also capable of the reverse transformation (i.e., linear to rotary). Either way, mapping is controlled by the screw’s lead — the distance the nut travels in one revolution. Lead-screws are subject to backlash.

Cabled drums convert between linear and rotary motion according to the drum circumference, since one turn of diameter D wraps or unwraps a length πD of cable. An external force (e.g., supplied by a spring or a weight) might be necessary to maintain cable tension.

Pulleys can direct a string pot’s cable over a complex path to a motion source. Mapping is 1:1 unless the routing provides a mechanical advantage.

Pulleys and belts transmit rotary motion scaled according to relative pulley diameters. The belt converts between linear and rotary motion. (See Figure 6.6(a)) The empty area between pulleys provides a convenient passageway for other components. Sprocket wheels and chain have similar characteristics. Matched pulley-belt systems are available that operate with negligible slip, backlash, and stretch.

Cams map rotary motion into linear motion according to the function “programmed” into the cam profile. See [10] for more information.

Linkages can be designed to convert, scale, and transmit motion. Design and analysis can be quite complex and mapping characteristics tend to be highly nonlinear. See [11] for details.

Flexible shafts transmit rotary motion between two non-parallel axes with a 1:1 mapping, subject to torsional windup and hysteresis if the motion reverses.

Conduit, like a bicycle brake cable or Bowden cable, can route a cable over an arbitrary path to connect a pot to a remote motion source. The conduit should be incompressible and fixed at both ends. Mapping is 1:1 with some mechanical slop. Lubrication helps mitigate friction.

A mechanism’s mapping characteristics impact measurement resolution and accuracy. Consider a stepper motor turning a lead-screw to translate a nut. A linear-motion pot could measure the nut’s position directly to some resolution. Alternatively, a rotary pot linked to the lead-screw could measure the position with increased resolution if the mechanism mapped the same amount of nut travel to considerably more wiper travel. Weighing the resolution increase against the uncertainty due to backlash would determine which approach was more accurate.

Implementation

Integrating a pot into a measurement system requires consideration of various design issues, including the impact of the pot’s physical characteristics, error sources, space restrictions, and wire-routing. The pot’s shaft type and bearings must be taken into consideration and protected against excessive loading. A good design will:

•Give the pot mount the ability to accommodate minor misalignment

•Protect the shaft from thrust, side, and bending loads (i.e., not use the pot as a bearing)

•Provide hard limit stops within the pot’s travel range (i.e., not use the pot’s limit stops)

•Protect the pot from contaminants

•Strain-relieve the pot’s electrical connections

A thorough treatment of precision design issues appears in [12].

Coupling to the Pot

Successful implementation also requires practical techniques for mechanical attachment. A string pot’s cable terminator usually fastens to other components with a screw. For other types of pots, coupling technique is partly influenced by the nature of the shaft. Rotary shafts come with various endings, including plain, single-flatted, double-flatted, slotted, and knurled. Linear-motion shafts usually terminate in threads, but are also available with roller ends (to follow surfaces) or with spherical bearing ends (to accommodate misalignment). With care, a shaft can be cut, drilled, filed, threaded, etc.

© 1999 by CRC Press LLC

In a typical measurement application, the pot shaft couples to a mechanical component (e.g., a gear, a pulley), or to another shaft of the same or different diameter. Successful couplings provide a positive link to the shaft without stressing the pot’s mechanics. Satisfying these objectives with rotary and linearmotion pots requires a balance between careful alignment and compliant couplings. Alignment is not as critical with a string pot. Useful coupling methods include the following.

Compliant couplings. It is generally wise to put a compliant coupling between a pot’s shaft and any other shafting. A compliant coupling joins two misaligned shafts of the same or different diameter. Offerings from the companies in Table 6.4 include bellows couplings, flex couplings, spring couplings, spider couplings, Oldham couplings, wafer spring couplings, flexible shafts, and universal joints. Each type has idiosyncrasies that impact measurement error; manufacturer catalogs provide details.

Sleeve couplings. Less expensive than a compliant coupling, a rigid sleeve coupling joins two shafts of the same or different diameter with the requirement that the shafts be perfectly aligned. Perfect alignment is difficult to achieve initially, and impossible to maintain as the system ages. Imperfect alignment accelerates wear and risks damaging the pot. Sleeve couplings are available from the companies listed in Table 6.4.

Press fits. A press fit is particularly convenient when the bore of a small plastic part is nominally the same as the shaft diameter. Carefully force the part onto the shaft. Friction holds the part in place, but repeated reassembly will compromise the fit.

Shrink fits. Components with a bore slightly under the shaft diameter can be heated to expand sufficiently to slip over the shaft. A firm grip results as the part cools and the bore contracts.

Pinning. Small hubbed components can be pinned to a shaft. The pin should extend through the hub partway into the shaft, and the component should fit on the shaft without play. Use roll pins or spiral pins combined with a thread-locking compound (e.g., Loctite 242).

Set-screws. Small components are available with hubs that secure with set-screws. The component should fit on the shaft without play. For best results, use two set-screws against a shaft with perpendicular flats. Dimple a plain shaft using the component’s screw hole(s) as a drill guide. Apply a thread-locking compound (e.g., Loctite 242) to prevent the set-screws from working loose.

Clamping. Small components are also available with split hubs that grip a shaft when squeezed by a matching hub clamp. Clamping results in a secure fit without marring the shaft.

Adhesives. Retaining compounds (e.g., Loctite 609) can secure small components to a shaft. Follow manufacturer’s instructions for best results.

Spring-loaded contact. A spring-loaded shaft will maintain positive contact against a surface that moves at reasonable speeds and without sudden acceleration.

Costs and Sources

Precision pots are inexpensive compared to other displacement measurement technologies. Table 6.5 lists approximate costs for off-the-shelf units in single quantity. Higher quality generally commands a higher price; however, excellent pots are often available at bargain prices due to volume production or surplus conditions. Electronic supply houses offer low-cost pots (i.e., under $20) that can suffice for short-term projects. Regardless of price, always check the manufacturer’s specifications to confirm a pot’s suitability for a given application.

Table 6.6 lists several sources of precision pots. Most manufacturers publish catalogs, and many have Web sites. In addition to a standard product line, most manufacturers will custom-build pots for highvolume applications.

TABLE 6.5 Typical Single-quantity Prices ($US) for Commercially Available Pots

© 1999 by CRC Press LLC

TABLE 6.6 Sources of Precision Pots

© 1999 by CRC Press LLC