Synthesis and Analysis of a Chebyschev’s Straight Line Four-Bar Linkage for Generating a Minimum Jerk Velocity Profile

Abstract

The interaction between human and passive, constraint-based path generating mechanisms has been scarcely studied. When it comes to rehabilitation robots, output trajectories and/or forces are achieved mainly as a result of actuation on all joints, since they form an open kinematic chain. On the other end, there exists a wide range of mechanisms that can trace complex trajectories primarily due to mechanical constraints in their topology and structure. Probably the simplest example is the four bar linkage, a widely used 1-DOF mechanism. It consists of a driving link, a driven link, and a coupler which connects the two. As the input link rotates, each point on the coupler link traces a unique trajectory in space, called a coupler curve. Ideally, the linkage dimensions can be chosen so that a near-natural hand trajectory is generated for a specific task. As a first step, in this work a straight line generating four-bar mechanism, namely the Chebyshev’s linkage is considered for generating a natural bell-shaped velocity profile, as prescribed by the Minimum-Jerk-Model. Initially the mechanism is synthesized for producing a straight line trajectory of a desired length. Kinematic and kinetostatic analysis is performed in order to determine the required input torque necessary for achieving the desired spatio-temporal profile. The main objective is to determine whether this input torque can approximated by a series of linear torsional springs that can be installed on the pivoted side of the input link.