A general method for the optimal synthesis of mechanisms using prescribed instant center positions

Although many methods have been proposed in the literature for rigid-body guidance synthesis none of them establishes the position of the instant center (IC) and the centrode as a design requirement. In many cases, practical designs of mechanisms need to accurately establish the position of the IC and the centrode. Due to the lack of methods tackling this problem directly, designers try to approach it indirectly. In other words, they establish the position of the desired rigid-body to obtain the desired position of the IC. However, small errors in the position of the rigid-body may lead to significant errors in the position of the IC and a trial-and-error process is necessary to achieve accuracy. The main difficulty in implementing the centrode in a synthesis approach is how to formulate the IC conditions in an optimization method. This paper presents a synthesis approach based on optimization in which the location of the centrode is included in the objective function. The formulation developed in the paper uses exact differentiation to obtain the descent direction and can be applied to any type of planar mechanism. Multi-objective optimization is also possible, including different design criteria in the target function. Several examples are provided to demonstrate the robustness, accuracy and efficiency of the new approach.