Kinematic synthesis and analysis of the rack and pinion mechanism for planar path generation and function generation for six precision conditions

Abstract

The rack and pinion mechanism is synthesized for generating both three prescribed path points with input coordination and three positions of function generation. This mechanism has a number of advantages over the four bar linkage. First, since the rack is always tangent to the pinion, the transmission angle is always the same (optimum) value of 90° minus the pressure angle of the pinion. Second, with both translation and rotation of the rack occuring, multiple outputs are available. Other advantages include the generation of monotonic functions for a wide variety of motion and nonmononotomic 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 a completely rotatable input crank and others. The method of solution developed in this work utilizes the complex number method of mechanism synthesis and the solution is programmed on a VAX 11 785 computer and is being made available to interested readers.