Computational issues in the synthesis of parallel mechanisms for the modelling of articular human joints

Mathematical models of human articular joints proved to be of great theoretical and practical relevance. They play, indeed, a fundamental role in many important issues such as preplanning surgical operations, diagnosis procedures and prosthesis design. Many planar and spatial models have been proposed in the literature. Planar models are generally simpler but they provide very limited information, especially for the design of advanced (sophisticated) prostheses. On the other hand, spatial models are very involved and quite often the model results are not easy to be used practically. Recently, we developed a procedure which aims at defining human joint models that can take into account the main (and many) anatomical structures of the joint such as ligaments and articular bone surfaces. The models are based on the use of equivalent spatial parallel mechanisms that mimic both the joint anatomical structures and the joint motion. The procedure to synthesize these mechanisms has however some critical points which deserve a great attention in order to be successfully overcome. This study focuses on the main mathematical issues involved in the procedure and on the strategies the authors have devised in order to overcome these problems and let the algorithms to be stable and efficient. In particular, the treated issues are the avoidance of singularity problems in the solution of non-linear systems for the synthesis of the equivalent mechanisms, and the definition of efficient algorithms to converge to a satisfactory solution by recursive optimization procedures. Examples are reported for the definition of joint models of the lower limb (knee and ankle) that show the efficiency of the adopted strategies.