The mechanical side of the “lost motion” problem has many complexities. To some extent mechanical systems have very defined properties which are easy to characterize. The performance of a gear box, for example, is well understood and it is usually very consistent over time. Because these systems have been around for a long time, we are even able to characterize wear and measure performance over time in critical systems. The gear industry has done an excellent job of understanding the unique material behaviors of gear systems and how to optimize the manufacture of its products.
Geared systems are designed around a curved sliding geometry called the involute spline shape for spur gears. These systems are cut using complex cutting and grinding tools which are required to produce the geometry. Accuracy in gear systems is measured in arc-minutes, 6oths of a degree of angle. The America Gear Manufacturing Association publishes standards for these systems and in the case of industrial planetary gears, backlash error can be as low as 4 arc minutes. Really low backlash, but not zero.
As with all things motion control, there are some clever mechanical workarounds for the backlash problem. The double enveloping worm gear was developed a few years back to eliminate backlash in the geometry of the worm and spur gear set. Traditionally worm and spur gear reducers have been the workhorse of industry, but the traditional geometry of these systems has been typically low efficiency and high backlash. So the emergence of high efficiency, low backlash worm & spur reducers offers high reduction ratio and low cost in a very compact package.
Some systems rely on “anti-backlash” mechanisms within the assembly to minimize lost motion. Split spur gears with springs that push the halves of the gear to either side of the load gear teeth are a common solution. In the lead screw industry similar solutions exist where the drive nut is composed of two segments that are spaced apart with a spring.
Mechanical systems like gears are thought of as rigid bodies. But there is a whole class of systems which are torsionally compliant. Couplings between motors and loads are intentionally compliant to reduce shock to the load. Most importantly torsional compliance needs to be considered as a form of lost motion. The loss of motion is temporary as the load inertia is accelerated. Once the system comes up to speed the compliance goes away. Examples of this type of system would be cycloidal reducers.
Some manufacturers like to refer to their products as “zero backlash” based on a compliant mechanism . The most positive of these is the flex spline type reducer. These are made of very thin steel rings with splines on mating surfaces. The outer spline is rigid and the inner spline flexes with several teeth engaged on each side of the circle. They are very power dense and very precise. Since they are typically hollow, lightweight and fairly stiff, they are very popular in the robot industry. However, there is a little bit of flexure, or spring behavior involved, which, contrary to the vendor claims, is lost motion.
In all cases where the mechanical system has torsional compliance, be it spring based or rolling element, the compliance constitutes lost motion. Consider making a 2 axis linear machine using mechanical solutions that are slightly compliant to draw a circle. The two axes load behaviors are out of phase with each other and the compliant nature of the axes will cause circularity error that cannot be controlled. As speed increases, the error will increase as well.
Not all anti-backlash systems are created equal.