Function generation synthesis with a 2-DoF overconstrained double-spherical 7R mechanism using the method of decomposition and least squares approximation

Abstract

This study addresses the approximate function generation synthesis with an overconstrained two degrees-of-freedom double spherical 7R mechanism using least squares approximation with equal spacing of the design points on the input domain. The 7R mechanism is a constructed by combining a spherical 5R mechanism with a spherical 4R mechanism with distant centers and a common moving link and then removing the common link. This construction allows the analysis and synthesis of the re-sulting single-loop mechanism by decomposing it into fictitious 5R and 4R loops. The two inputs to the mechanism are provided in the 5R loop and the output is in the 4R loop. The fictitious output of the 5R loop is an input to the 4R loop this intermediate variable is used to also decompose the function to be generated. This decomposition provides the designer extra freedom in synthesis and enables de-creasing the error of approximation. A case study is presented at the end of the study where the 7R de-sign is compared with an equivalent spherical 5R mechanism; hence the advantage of the 7R mecha-nism is demonstrated.