Redundant singularities versus constraint singularities in parallel mechanisms

The paper discusses the redundant singularities versus constraint singularities in relation to the main structural parameters of parallel mechanisms. The formulae of mobility, connectivity, overconstraint and redundancy of parallel mechanisms, recently proposed by the second author of this paper, are used to characterise these singularities and the transition phase between them. By using these formulae, the main properties of three types of singularity are identified. A new combined constraint-redundant singularity is defined and characterised, in connection with constraint and redundant singularities. A reconfigurable eight-bar single-loop mechanism is used to illustrate the three types of singularities. This mechanism has an interesting property to continually transit from one type of singularity to another by remaining always in a singular configuration. The properties of the redundant and constraint-redundant singularities are defined in this paper in relation to the four main structural parameters of a mechanism.