Classification and analysis of constraint singularities for parallel mechanisms using differential manifolds

This paper presents investigations into classification and analysis of constraint singularities for parallel mechanisms. Parallel mechanisms (also called parallel manipulators or parallel robots) have wide applications in industry. The singularities tremendously affect their applications. Existing research works show that constraint singularity causes a mechanism to have instantaneous degree-of-freedoms (DoFs) or bifurcated finite motions. However, the intrinsic differences among the conditions under which the specific constraint singularities happen have not been discussed. This paper is focused on these topics by using differential manifolds as mathematical tools. Firstly, the general mathematical models of parallel mechanisms are formulated by respectively describing their finite motions and instantaneous motions in forms of differential manifolds and their tangent spaces. Then, parallel mechanisms having bifurcated finite motions and instantaneous DoFs are modelled accordingly, and the constraint singularities are thus classified into two kinds by considering their influences on motions of mechanisms in both finite and instantaneous motion levels. Finally, two examples are given to further illustrate the theoretical analysis. This paper lays foundations for mathematical modelling and applications of parallel mechanisms with constraint singularities.