Abstract
The forward kinematic problem (FKP) of the 3-RRS parallel manipulator is solved by means of the Newton-homotopy continuation method. The closure equations are formulated in the three-dimensional Euclidean spaces considering the coordinates of the centers of the spherical joints as unknown variables. The method is easy to follow and unlike the classical Newton-Raphson method it allows finding all the solutions of the FKP. A case study is included in the contribution in order to confirm the correctness of the method. In that concern, the numerical results obtained by means of the proposed method are verified with the aid of two different approaches such as the application of commercially available software like Maple16™ and the application of the PHCpack, a general purpose solver for polynomial systems based on homotopy continuation.
Highlights
A parallel manipulator is a mechanical device composed of a moving platform and a fixed platform connected each other by means of at least two kinematic chains or legs
This work deals with the forward kinematic problem of the 3-RRS parallel manipulator where R and S stand for revolute and spherical joint, respectively, which is a robot able to perform the 2R1T motion
Zhao et al [5] developed a family of metamorphic parallel manipulators based on the topology of the 3-RRS parallel manipulator in which the substitution of spherical joints by different kinematic devices plays a central role in order to modify their mobility
Summary
A parallel manipulator is a mechanical device composed of a moving platform and a fixed platform connected each other by means of at least two kinematic chains or legs. Compared with their serial counterparts, parallel manipulators bring us interesting advantages like higher accuracy and stiffness as well as the possibility to place the servo motors near to the fixed platform. This work deals with the forward kinematic problem of the 3-RRS parallel manipulator where R and S stand for revolute and spherical joint, respectively, which is a robot able to perform the 2R1T motion. Some conclusions are given at the end of the contribution
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