Mixed synthesis method of motion and path of planar four-bar linkages

Rui Wu,Hailong Liang,Ruiqin Li,Fengping Ning

doi:10.5194/ms-12-443-2021

Abstract

Abstract. The mixed synthesis of motion and path generation, which is also known as the Alt–Burmester problem, is an attractive problem for study. However, such a problem for the four-bar linkages which possess more than M poses (M>5) and mixed N path points has not been well-solved. In this work, a mixed synthesis method is developed for planar four-bar linkages to cope with the above problem. The developed method can quickly select an optimal combination that contains five poses and N points by using the conic filtering algorithm, which is based on the similar characteristics of the value and direction between the conic and coupler curves in a certain neighborhood. Next, the selected five poses are substituted into a simplified equation system of motion synthesis which includes four equations and four variables to solve the parameters of the planar four-bar linkage. Finally, a case is provided to validate the effectiveness of the developed method in the mixed synthesis problem.

Highlights

Kinematics problems are categorized into three kinds of problems that can be solved by three different solutions (Nolle, 1974; Li et al, 2020)
Brake et al (2016) used a numerical algebraic geometry method to study all the Alt–Burmester problems with finite solutions under the case 2M + N ≤ 10 (M poses, N path points), where each solution set under the general case has dimensions and orders from zero to eight
Sharma et al (2019) presented an analytical method based on the Fourier approximation to deal with the mixed synthesis problems, where the harmonic decomposition of the closedloop equation represents the analytic relationship between the direction and the path

Summary

Introduction

Kinematics problems are categorized into three kinds of problems that can be solved by three different solutions (Nolle, 1974; Li et al, 2020). Fall into a class of problems that cannot be well-solved, such as the mixed synthesis problem with motion and path constraints. Path, and function generation are three categories of linkage synthesis problems that have three different synthesis equations (Zhao et al, 2016b; Pennestri and Valentini, 2018). 1990; Cabrera et al, 2011; Guigue and Hayes, 2016) Another path synthesis problem, the coupler-curve synthesis, has been studied with a fully analytical method and a method that combines both the analytical and graphical methods (Wu et al, 2021; Bai et al, 2021). A mixed synthesis method based on the equation of motion synthesis is proposed.

Conic filtering algorithm

Problem formulation

Case study

This work

Conclusions