Motion System Design
Handling the curves

Handling the curves

Sometimes a linear application will throw you a curve. To get back on track, try slides and races that provide linear motion in the round and that can link linear applications to curved applications.

Not all linear motion applications consist of straight lines. Some applications require an occasional curve or even circular motion. Spray painting, pick and place, rotary assembly, and multi-station assembly machines are typical applications that may require motion executed in the round, Figure 1.

One type of curved linear-motion system uses V-ball bearings. It has opposing female bearings with V-shaped outer rollers in a two-and-two arrangement. The bearings ride on a track with matching zone-hardened V-shaped rails. A carriage plate on top of the two-and-two bearings is the mounting platform, Figure 2. Thus, the carriage assembly effectively runs on eight line-contact points on a track with varying circumferential diameters.

Two types of carriages are available. When using a fixed segment of a ring, fixed center carriage plates are the most popular. A bogie carriage, Figure 3, is best for use around S-bends, slideways with differing bend radii, and curves where looseness in the movement between straight and curved sections is not desirable. The bogie carriage runs on swivel bearings, which operate on a principal similar to that used in train and tram bogies to negotiate bends in the track. The two types or carriages facilitate the flexibility of V-ball-bearing track systems. It is not necessary to mount these systems to a machined flat surface unless high accuracy is required.

V-ball bearing track systems are best suited to light loads — direct loads from 120 to 3,800 N (26.98 to 854.38 lb) and moment loads from 0.6 to 220 Nm (0.53 to 1,946.90 lb-in.)in a lubricated system. Refer to manufacturers’ tables for precise load handling capabilities.

Rings and segments

Often when the application calls for a curved linear system, an engineer is looking for pure radial movement, such as that found in tool changing mechanisms, measurement of turbine blades, rotating manipulators, movement of prisms in laser measurement machines, and rotation of photographic cameras. These applications require a segment of a ring, typically available in 90 or 180 deg, or a complete ring with 360 degrees of rotation, Figure 1.

Rings offer stability with support as near to the load as possible. In spraying applications, for example, a paint nozzle mounts on a fixed center carriage plate that tracks the curvature of the sprayed product to ensure even coating. A gearcut rack on the outside diameter of the register face of the ring serves as the drive mechanism. (The gearcut rack can also be placed on the internal register face of the ring).

A ring is typically mounted to a base with the carriage assembly as the sliding member. However, the slide ring can be the rotating element by locating its center with two concentric V-ball bearings and at least one adjustable eccentric bearing. Additional eccentric bearings can be added to achieve higher load capacity and stability.

Track systems

Once the ring selection is made, engineers need the ability to link any linear and curved segments to make a track system. Some linear slideways are available in lengths to 4 m; for longer lengths, slide segments are matched and butted together. Using standard tracks and ring or segments of rings, hundreds of arrangements are possible.

The most popular track system is the oval, with two equal length linear slides and two 180 deg segments. Several carriages may run on the track simultaneously, (also referred to as a continuous motion system) using a toothed timing belt with location lugs to drive the carriages. This track arrangement is used in micro-chip X-ray machines, automotivecomponent assembly, biscuit cutting, food packaging, and box-filling machines.

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These continuous motion systems, with multiple carriages running continuously on a track and carrying parts to various manufacturing operations, link such operations together and reduce dead time. Continuous motion is also less arduous on drive mechanisms and motors — the motor only needs to go in one direction so there are no large inertia forces to overcome in stopping and reversing.

Clean track

V-ball bearing systems can run dry or lubricated. Some applications, such as nuclear and food applications, won’t permit the use of oil lubrication. So the ability to run dry can be important to the design of a system. To prolong system life, by as much as 150% in some cases, engineers can add lubricator blocks, which have sprung loaded felt pads that sit in a reservoir of oil and contact the male V of the ring slide. Every time the ring slide rotates it is wiped with oil, which is also imparted to the female V of the bearing surfaces.

These systems are not affected by debris along the V-shaped rails or opposing V-shaped rollers, Figure 4. The differential circumferences between the inner and outer diameters of the bearing surfaces cause a self cleaning action which throws off debris, from small dust particles to large chunks.


For rings or segments of rings, it is possible to achieve circular motion with radial run-out no greater than 0.05 mm per 360 deg (pro rata over angle of segment). Axial run-out is 5 microns.

For multiple carriage track systems, the greatest repeatibility error is in the direction of travel and is dependent on the play in the drive mechanism. However, it is possible to achieve repeatability with 0.2 mm with a belt-driven system.

With all radial motion there is an extra load to consider — centrifugal force. The force is proportional to the square of the tangential velocity. If you double the carriage speed, you quadruple the force. It is also inversely proportional to the radius, so if you double the radius, you half the force. Conversely, the smaller the radius, (tighter you corner) the greater the force. Often, this force will also cause a moment load about the carriage plate.

How to calculate load and life

Several factors determine the load capacity and life expectancy of a ring, segment, and track system:
• Size of the ring.
• Size and number of bearing assemblies.
• Presence of lubrication.
• Magnitude and direction of the loads.
• Speed of operation.
• Length of the traversed path; life is shortened when length of path is below 0.2 m.

Here’s how to calculate the life expectancy of a track system consisting of two curved segments and two linear segments linked as an oval, Figure 5.

The carriage carries a dead weight such that the mass of the load and the carriage together is a total of 40 kg whose center of mass is over the middle of the carriage. The center of mass is 80 mm above the slides. The speed of operation is 0.7 m/s and the system is lubricated.

Referring to Figure 6. A value of 0.49 for the life factor LF is then entered into the nomogram for lubricated systems, Figure 7, to obtain the linear life.

Reading from the nomogram, the corrosponding value to 0.49 is 2,900 km. Thus this carriage with its load has an expected life of 2,900 km.

Pat Shue is senior applications engineer, Bishop-Wisecarver Corp., Pittsburg, Calif.

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