Effect of Compliance and Backlash on the Output Speed of a Mechanical Transmission System

A dynamic model to describe the effect of compliance in a transmission system is presented. Analysis of this model shows that it is desirable to use feedback from driver-side of the transmission system. This model is extended to include the effects of both compliance and backlash in a mechanical transmission system. The proposed model considers compliance (which may be either due to the elasticity of the shafts or belt in a belt-pulley transmission system) and backlash appearing in series in a drive system. In contrast to the classical backlash model which considers both input and output to the backlash as displacements, the proposed model considers (torque) force as input to the backlash and (angular velocity) velocity of the driven member as the output of the backlash. Thus, the proposed model does not assume that the load is stationary when contact is lost due to backlash width, i.e., momentum of the load is taken into account. Using the proposed model, a bound on the speed error due to the presence of backlash is derived. Experiments were conducted on a rectilinear mass-spring system platform, which has a provision to change the backlash width by a known value. Experiments were conducted with different backlash widths and a velocity error bound was computed. The error bound obtained from the experimental results agrees with the theoretically computed bound.