Despite widespread industrial applicatzon of harmonic drives, the source of some elastokinetic phenomena and their impact on overall system behavior has not been fully addressed thus far. Some of these phenomena severely influence the behavior of robot arms, both in free and constrained motions, when the end effector is in contact with an environment. The primary goal of this study is to derive an effective, control-oriented model of a harmonic-drive-based robot joint. Systematic observations of an experimental robot with harmonic drives has revealed that the harmonic drive could not entirely transmit the input torque to the output shaft, due to a nonlinear meshing process between the flexible and circular spline teeth. The torque transmitted to the output shaft might saturate at a much lower value than expected (e.g., motor torque multiplied by the gear ratio). This phenomenon may severely influence the system behavior, par ticularly in force/impedance control tasks when full joint-torque capacity and wide bandwidth are needed. To understand the harmonic-drive behavior, as well as to derive a convenient form of its model, we have shown restrained motion experi ments to be much more useful than free-motion experiments.

In this article, we also introduce mathematical models and describe experiments related to other physical phenomena, such as nonlinear stiffness, hysteresis, and soft windup. The goal of our modeling strategy was not to develop a precise and possi bly complicated model, but to generate an appropriate model that could be easily used by control engineers to improve joint behavior To visualize the developed model, equivalent mechan ical and electrical schemes of the joint are introduced. Finally, a simple and reliable estimation procedure has been established for obtaining joint parameters, to ascertain the integrity of the proposed model.