Function synthesis of the planar 5R mechanism using least squares approximation

Abstract

In this paper, the problem of function generation synthesis of planar 5R mechanism is studied using the least squares approximation method with equal spacing of the design points. The study represents a case study for analytical function generation of multi-degrees-of-freedom systems. The planar 5R mechanism is designed with a fixed input joint and a moving input joint adjacent to the first input, whereas the remaining fixed joint is the output joint. The input/output relationship of the mechanism is expreseed as an objective function in polynomial form with four unknown construction parameters. The objective function involves nonlinearities, however the problem is linearized using Lagrange variables. The linear system is solved and finally the construction parameters of the mechanism are determined. A numerical example is presented as a case study.