An Automatic Method for Finding the Assembly Configurations of Planar Non-Single-Input-Dyadic Mechanisms

Abstract

This paper examines the problem of identifying the assembly configurations (ACs), also called circuits, of planar non-single-input-dyadic (NSID) mechanisms. An SID mechanism is a multi-loop mechanism which can be defined by adding one loop at a time such that the mechanism has one degree of freedom (DOF) after each loop is added. An NSID mechanism is any mechanism that does not meet the SID criterion. This includes all multi-DOF mechanisms, and some complex single-DOF mechanisms. An automatic method is presented which allows a computer to determine the ACs of an NSID mechanism. For single-DOF mechanisms, the ACs are represented by curves drawn in a plane represented by two joint variables. For multi-DOF mechanisms, the ACs consist of one or more regions in the plane, which are defined by the curves that bound them. The automated method finds these bounding curves, and then determines which curves belong to the same region, and which regions belong to the same AC. Mechanisms with pin joints and sliding joints are considered.