The Influence of Special Positions on the Rigidity of Parallel Structure Mechanisms

Abstract

Due to a sharp increase in the accuracy of manufacturing and quality control of mechanical engineering products, robots based on mechanisms with closed-loop kinematic chains have become a promising area of engineering. One of the advantages of parallel structure mechanisms over serial mechanisms is their increased rigidity. The absence of patterns in the change of rigidity in the working zone and the influence of the so-called special positions necessitate the development of new methods of optimization synthesis of the mechanism. This paper presents an approach based on the Jacobian matrix using which it is possible to determine rigidity in the worst direction of the external force application in each point of the working zone. The same approach can also be used for determining the shape and size of the effective working zone. An example of a flat five-chain mechanism is used to demonstrate the application of the method and obtain a matrix of chain rigidity, construct the parallelogram of forces and determine rigidity distribution in the working zone. It is shown that when approaching a special position, the rigidity of the mechanism decreases ten-fold, and in the special position it equals a zero. The proposed method can be used for optimizing the geometrical parameters of the mechanism on the conditions of maximising the effective working zone.