The paper presents the kinematic synthesis of a symmetric parallel platform supported by three RRS serial chains. The dimensional synthesis of this three degree-of-freedom system is obtained using design equations for each of three RRS chains obtained by requiring that they reach a specified set of task positions. The result is 10 polynomial equations in 10 unknowns, which is solved using polynomial homotopy continuation. An example is provided in which the direction of the first revolute joint (2 parameters) and the z component of the base and platform are specified as well as the two task positions. The system of polynomials has a total degree of 4096 which means that in theory it can have as many solutions. Our example has 70 real solutions that define 70 different symmetric platforms that can reach the specified positions.

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