Kinematic Synthesis and Analysis of the Rack-and-Gear Mechanism for Four-Point Path Generation With Prescribed Input Timing

Abstract

The rack and gear mechanism is synthesized for generating four prescribed path points with input coordination. This mechanism has a number of advantages over the well-known four-bar linkage. First, the transmission angle is always at its optimum value of 90 deg since the rack is always tangent to the gear. Second, with both translation and rotation of the rack occurring, multiple outputs are available. Other advantages include the generation of monotonic functions for a wide range of motion and nonmonotonic functions for the full range of motion as well as nonlinear amplified motions. In this work, the mechanism is made to satisfy a number of practical design requirements such as having a completely rotatable input crank, elimination of the branching defect and others. The method of solution developed in this work employs the Burmester Four-Precision-Point Algorithm with additional relations utilizing the Complex Number Method of Mechanism Synthesis. The solution is programmed on the DEC/PDP 11/70 and is available to interested readers.