In this paper, we study the problem of rational motion interpolation under kinematic constraints of spatial SS open chains. The objective is to synthesize a smooth rational motion that interpolates a given set of end effector positions and satisfies the kinematic constraints imposed by spatial SS open chains. The kinematic constraints under consideration define a constraint manifold representing all the positions available to the end effector. By choosing dual quaternion representation for the displacement of the end effector, the problem is reduced to designing a smooth curve in the space of dual quaternions that is constrained to lie inside the constraint manifold of the spatial SS open chain. An iterative numerical algorithm is presented that solves this problem effectively. The results presented in this paper are extension of our previous work on the synthesis of piecewise rational planar and spherical motions for open and closed chains under kinematic constraints.

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