Dynamic scaling of trajectories for robots with elastic joints

The classical dynamic scaling property of robot trajectories is analyzed in the case of presence of elastic transmissions. We present a technique for recovering the fastest motion under torque constraints, when uniform time scaling is used along a given path. The scaling algorithm is based on the solution of a complete quartic polynomial equation, which reduces to a biquadratic one in the absence of viscous friction. Consequences on the organization of inverse dynamics computation are pointed out. Numerical results are reported for a planar 2R arm, illustrating the differences that arise with respect to the fully rigid case