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This paper presents a new joint coined as the rT joint and proposes two types of metamorphic parallel mechanisms assembled with this rT joint. In the first type, the mechanism changes its topology by turning the rT joints in all limbs into different configurations. This change in mobility is completed by two cases illustrated by a 3(rT)PS metamorphic parallel mechanism having variable mobility from 3 to 6 and a 3(rT)P(rT) parallel mechanism having various configurations including pure translations, pure rotations, and mobility 4. In the second type, a central strut with the rT joint is added in a parallel mechanism. The variable mobility of the mechanism results from the topological change of the central (rT)P(rT) strut. This is illustrated in a 3SPS-1(rT)P(rT) metamorphic parallel mechanism, which changes its mobility from 4 to 5. It is demonstrated in mobility analysis that the change in local mobility of each limb results in the change in the platform mobility that a metamorphic process can be achieved. This particular analysis leads to advancement of improved Grübler–Kutzbach criterion by introducing the local mobility factor in the mobility analysis.

The theory of dual quaternion and its use in serial mechanisms are described in this paper. A closed-form solution to the inverse kinematic analysis of the general 7-link 7R mechanism is presented. Dixon's resultant is used and the input-output equation is expressed in the form of a 6 × 6 determinant equated to zero, and the formulae to determine other angular displacements are expressed in the closed form. Numerical example confirms these theoretical results. The whole process is very simple and easy to program, which supplies a new method for the real use of the 7R mechanism. Downloaded fromThe inverse kinematics analysis of the 7R mechanism is that s i , α i , a i , and θ 7 are known parameters and Fig. 2 The general 7-link 7R mechanism

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