Direct Kinematics Solution of 3-RCC Parallel Robot using a Semi-Analytical Homotopy Method

Parallel robots are closed-loop mechanisms presenting very good performances in terms of accuracy, rigidity, and the ability to manipulate large loads. Inverse kinematics problem for most parallel robots is straightforward, while the direct kinematics is not. The latter requires the solution of the system of nonlinear coupled algebraic equations and has many solutions. Except in a limited number of these problems, there is difficulty in finding exact analytical solutions. So these nonlinear simultaneous equations should be solved using some other methods. Continuation or path-following methods are standard numerical techniques to trace the solution paths defined by the Homotopy. This paper presents the direct kinematics solutions for a 3RCC parallel robot by using a semi-analytical Homotopy method called Homotopy Continuation Method (HCM). The HCM has some advantages over the conventional methods and alleviates drawbacks of the traditional numerical techniques, namely; the acquirement of good initial guess values, the problem of convergence and computing time. The direct kinematic problem of the 3RCC parallel robot leads to a system of nonlinear equations with 9 equations and 9 unknown parameters. The proposed method solved these nonlinear equations and extracted all the 36 solutions. Results indicate that this method is effective and reduces computation time in comparison with the Newton–Raphson method.