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首页> 外文期刊>Mathematical Problems in Engineering >An Application of the Newton-Homotopy Continuation Method for Solving the Forward Kinematic Problem of the 3-RRS Parallel Manipulator
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An Application of the Newton-Homotopy Continuation Method for Solving the Forward Kinematic Problem of the 3-RRS Parallel Manipulator

机译：牛顿同态连续法在解决3-RRS并联机械手正向运动学问题中的应用

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摘要

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. Themethod 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 (TM) and the application of the PHCpack, a general purpose solver for polynomial systems based on homotopy continuation.
机译：通过牛顿-同伦连续方法解决了3-RRS并联机械手的正向运动学问题（FKP）。在三维欧几里得空间中，将球形关节中心的坐标视为未知变量来制定闭合方程。该方法易于遵循，并且与经典的牛顿-拉夫森方法不同，它可以找到FKP的所有解决方案。为了确认方法的正确性，案例中包含了一个案例研究。在这种情况下，借助于两种不同的方法来验证通过所提出的方法获得的数值结果，例如应用诸如Maple16（TM）的商业软件以及应用用于多项式系统的通用求解器PHCpack基于同伦连续性。

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