DEVELOPMENT OF THE TRI-LEVEL VARIABLE-RATE TRAJECTORY WITH DISCRETELY VANISHING SHOCK FOR OPTIMUM DESIGN

The tri-level variable rate trajectory is a general motion which can be applied to programmable controllers, robotic manipulators, mechanisms, and mechanical devices where the input crank orientation, velocity, and acceleration vary with time. In the work presented here, the tri-level variable rate trajectory is an extension of the variable-rate trans-symmetric motion developed by the first author in 1984. That motion and the one developed here consist of discrete segments of constant and linearly varying accelerations occurring over specified time intervals, thereby providing versatile programmable trajectories with several advantages over the constant polynomial trajectories used in robotics.