In this paper a new computational technique for the inverse position problem of a 7R robot is presented. Instead of reducing the problem to one highly complicated input-output equation, we work with a system of 10 very simple polynomial equations. We show the total degree of the system is 16, in agreement with previous works. Moreover we present a numerical example confirms the technique. The whole process is simple and easy to program.
In this paper a new algorithm to compute all the closed-form inverse kinematics solutions of a spatial serial robot. Based on the method, A 16th degree univariate polynomial of the spatial serial robot is obtained without factoring out or deriving the greatest common divisor. We also obtain all the closed-form solutions for the inverse kinematics of the robot. Finally a numerical example is given to demonstrate the algorithm process.
The parallel robotic manipulator has attracted many researchers’ attention and it also has growing applications to different areas. In this paper an algebraic method for solving the direct kinematics analysis problem for a parallel robotic manipulator. Based on the presented algebraic method, the problem is derived into a 40th degree univariate polynomial. All complete sets of 40 solutions to the problem are obtained. The proposed method is exemplified by a numerical example.
Stewart platform manipulator robot is a six degree of freedom, parallel manipulator, which consists of a base platform, a mobile platform and six limbs connected at six distinct points on the base platform and the mobile platform respectively. The direct position analysis problem of Stewart platform relates to the determination of the mobile platform pose for a given set of the lengths of the limbs. In this paper, we present a concise algebraic method for solving the direct position analysis problem for the fully parallel manipulator with general geometry, often referred to as General Stewart platform manipulator. Based on the presented algebraic method, we derive a 40th degree univariate polynomial from a determinant of 20×20 Sylvester’s matrix, which is relatively small in size. We also obtain a complete set of 40 solutions to the most general Stewart platform. The proposed method is comparatively concise and reduces the computational burden. Finally the method is demonstrated by a numerical example.
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