Unified synthesis of planar linkages for function generation using the spring connected size-variable 3-blocks model

Abstract

The design of mechanical systems involves the synthesis of mechanisms in order to meet a set of kinematic requirements. Several synthesis methods, graphical, analytical and computer-aided technique, have been proposed for selecting and scaling mechanical devices. The objective is to guide a rigid body through a specified position, or to force a point on a linkage to trace out the desired trajectory curve, or to perform a specific input/output relationship. This paper is based on the last task, function generation, although the proposed method can be applied to any of them. In function generation, rotation or sliding motion of input and output links must be correlated. Extensive research has been given to the synthesis of mechanisms for the purpose of function generation based on candidate mechanism layout. However, in the initial design stage, the designer has to synthesize a combination of linkage topology and type of joints which may be best suited for a particular task. This problem may be solved by means of experience, intuition of designers. So, the systematic determination of the optimal topology and dimension of mechanisms is very important in the mechanism design process. In this paper, unified mechanism synthesis which covered the problem of type and dimensional synthesis of planar mechanisms with respect to the functional requirement of output motion is proposed. To perform the unified synthesis for function generation, a planar linkage is modeled as a set of size-variable three rigid blocks connected by zero-length translational springs with variable stiffness. The values of spring stiffness and size of rigid blocks yielding a desired output motion related to input motion at the end-effecter are found by using an optimization method. If spring stiffness values are appropriately chosen, any linkage mechanism connected by revolute and translational joints can be represented. A linkage dimensions are determined by related block size during the synthesis process.