Analysis of singularity planar multi-linkage mechanism of fourth order

Abstract

The planar multi-linkage mechanism of the fourth order, the output rocker of which implements an approximate stopping in one critical position is described in the article. The mechanism consists of three dyads passing through their limit positions in a single duty cycle. That is why the singularity problem is relevant for such mechanisms and should be studied to avoid jamming of links or the appearance of uncontrolled movements. The mathematical model is based on the theory of screws and contains the closed-loop equilibrium equations obtained for the investigated mechanism. Based on the obtained results of the geometry and singularity analyses, it is shown that there are eight different positions in which some joints stop momentarily and then their angular velocity direction changes.

Keywords

• planar multi-linkage mechanism
• singularity positions
• screw theory
• geometric analysis
• approximate stopping
• closed loop