Minimum Error Synthesis of Space Mechanisms for the Generation of Constrained and Unconstrained Screws

Abstract

The RSRC space mechanism is synthesized to generate constrained and unconstrained screws of the form ψ̂(θ) = ψ0 (θ) + εψ1 (θ), where θ is the input parameter. A variational principle is used to determine the dimensions of the optimum mechanism, where the dual error in the generated screw is minimized at a discrete set of design positions whose number vary from three up to 24 for each component of the screw. Parameters of constraints are introduced to eliminate the equations of constraints. These parameters provide that the related constraining conditions are satisfied exactly. They are also used to generate the rotation interval and advance-to-return time ratios in quick-return mechanisms exactly. Seven numerical examples are given, which include the design of 4R plane mechanism to generate screw of zero pitch having odd order instantaneous dwell: RSRC mechanisms to generate screws of infinite pitch, constant pitch, and variable pitch having odd and even order instantaneous dwells; RSRC (or RSCR) doublecrank mechanism having dwell in the output rotation, and quick-return mechanism.