In this work we present several parallel robots with reduced mobility whose platforms can change their subgroups of displacement when the robot is displaced continuously from one set of positions to another one. In some cases, also the number of degrees of freedom of the platform may change, in other cases, only the group of displacement or its invariant properties are modified. By using some results on mobility of single-loop kinematic chains based on the theory of the displacement groups, the way to synthesize these robots is discussed.

Starting from single-loop kinematic chains whose pairs present different connectivities when the chains are displaced in different positions, the paper shows how to assemble multiloop chains with numbers of degrees of freedom that change due to continuous variations in the position variables of the chains. This special mobility property is called kinematotropy. The paper provides a method (based on the displacement group theory) to form chains that allow any desired change in the number of degrees of freedom, with a sudden or gradual increment of this number. Several examples are presented and applications are discussed.

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