Abstract: The inverse kinematics of serial robots is a central problem in the automatic control of robot manipulators. The aim of this paper is to obtain a computational algorithm to compute the inverse kinematics problem of a spatial serial robot. We use a series of algebraic and numeric transformations to reduce the problem to a univariate polynomial equation. The results can be directly applied to symbolic calculations and decreased considerably the calculation time.

233

Authors: Yue Sheng Tan, Peng Le Cheng, Ai Ping Xiao

Abstract: Three basic sub-problems of screw theory are acceptable for some particular configuration manipulators’ inverse kinematics, which can not solve the inverse kinematics of all configuration manipulators. This paper introduces two extra extended sub-problems, through which all inverse kinematic solutions for 6-R manipulators having closed-form inverse kinematics can be gained. The inverse kinematic solution for a new particular configuration manipulator is presented.

250

Abstract: A new algebraic method for the solution of the forward displacement analysis of a parallel manipulator is presented in this paper. Based on the algebraic method, the problem of the forward displacement problem is reduced to a polynomial equation in a single unknown from a constructed matrix which is relative small in the size. From the univariate equation, all closed-form solutions of the different locations of the mechanism can be derived.

1061

Abstract: This paper presents a closed-form solution to determination of the position and orientation of a perspective camera with two unknown effective focal lengths for the noncoplanar perspective four point (P4P) problem. Given four noncoplanar 3D points and their correspondences in image coordinate, we convert perspective transformation to affine transformation, and formulate the problem using invariance to 3D affine transformation and arrive to a closed-form solution. We show how the noncoplanar P4P problem is cast into the problem of solving an eighth degree polynomial equation in one unknown. This result shows the noncoplanar P4P problem with two unknown effective focal lengths has at most 8 solutions. Last, we confirm the conclusion by an example. Although developed as part of landmark-guided navigation, the solution might well be used for landmark-based tracking problem, hand-eye coordination, and for fast determination of interior and exterior camera parameters. Because our method is based on closed-form solution, its speed makes it a potential candidate for solving above problems.

6

Authors: P.V. Jeyakarthikeyan, R. Yogeshwaran, Karthikk Sridharan

Abstract: This paper presents about generating elemental stiffness matrix for quadrilateral elements in closed form solution method for application on vehicle analysis which is convenient and simple as long as Jacobian is matrix of constant. The interpolation function of the field variable to be found can integrate explicitly once for all, which gives the constant universal matrices A, B and C. Therefore, stiffness matrix is no longer integration of the given functional, it is simple calculation of universal matrices and local co-ordinates of the element. So time taken for generation of element stiffness can be reduced considerably compared to Gauss numerical integration method. For effective use of quadrilateral elements hybrid grid generation is recommended that contains all interior element edges are parallel to each other (rectangle or square elements) and outer boundary elements are quadrilaterals with distortion. So in the Proposed method, the closed form and Gauss numerical method is used explicitly for interior elements and outer elements respectively. The time efficiency of proposed method is compared with conventional Gauss quadrature that is used for entire domain. It is found that the proposed method is much efficient than Gauss Quadrature.

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