Node to Node Requirements on the Synthesis of Mechanisms Using Minimum Distance Approach

The aim of this document is to show a method for the introduction of node to node requirements in the dimensional synthesis of mechanisms when using the minimum distance approach. The presented method allows one to introduce a requirement on the distance of two points belonging to different elements of the linkage, which has multiple practical applications such as the design of grippers. In order to do so, the minimum distance into both nodes is included in the error function for each synthesis point including these kind of requirements. The minimization of the minimum distance function is performed with a sequential quadratic programming algorithm. The required derivatives are obtained analytically to reduce computational cost and improve on convergence. The minimization of the synthesis problem is also solved here using an SQP method, but the error function has been developed taking into account the possibility of applying other methods such as genetic algorithms. The requirement is introduced as an additional term in the minimum distance function, thus allowing one to combine it to other types of requirements, such as node to point or node to line. Although in an initial stage of development, the method shows a good behavior in terms of convergence and computational efficiency. In order to demonstrate this, several examples of both the minimum distance problem resolution and also the synthesis resolution are presented.