A spherical wrist of the serial type is said to be isotropic if it can attaina posture whereby the singular values of its Jacobian matrix are all identicaland nonzero. What isotropy brings about is robustness to manufacturing,assembly, and measurement errors, thereby guaranteeing a maximum orientationaccuracy. In this paper we investigate the existence of redundant isotropicarchitectures, which should add to the dexterity of the wrist under design byvirtue of its extra degree of freedom. The problem formulation leads to asystem of eight quadratic equations with eight unknowns. The Bezout number ofthis system is thus 2^8 = 256, its BKK bound being 192. However, the actualnumber of solutions is shown to be 32. We list all solutions of the foregoingalgebraic problem. All these solutions are real, but distinct solutions do notnecessarily lead to distinct manipulators. Upon discarding those algebraicsolutions that yield no new wrists, we end up with exactly eight distinctarchitectures, the eight corresponding manipulators being displayed at theirisotropic posture.
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