In reality, clearances in the joints are inevitable due to the defects arising from manufacturing process, design tolerances, and wearing after a certain working period. It leads to a chaotic behaviour including the impact loads which results in an unpredictable response in the system. Since clearance introduces an additional uncontrollable degree of freedom to the manipulator, it causes error and could not be neglected in the manipulator design or analysis. In this study, the dynamic behavior of a planar mechanism with revolute joints, in the presence of clearances is investigated. The planar 3-RPR parallel manipulator with six revolute clearance joints is modelled in MSC.ADAMS software and the simulation results are presented. Moreover, the effects of clearance size on the dynamic characteristics of a planar mechanical system are analysed and compared. What is found out is the prediction of the dynamic error due to the joints clearance for this parallel robot. تفاصيل المقالة

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. تفاصيل المقالة

The length values selection for a determined type of linkage to achieve the necessary task, dimensional synthesis, is classified into three classes based on the mechanism’s task: function generation, path generation, and motion generation. The case considered in this study, Function generation synthesis, aims to create a relation between the angular motions of the input and output links of the mechanism. For this problem, a semi-analytical method called the Newton-HCM is used for numerical solutions, which combines Newton’s method with the semi-analytical Homotopy Continuation Method (HCM). Function generation synthesis of a planar four-bar linkage for four and five precision points is the main challenge of the current study, which is highly nonlinear and complicated to solve. Numerical examples of the function generation problem for a four-bar linkage with four and five precision points are presented and authenticate the excellent performance of the proposed algorithm. تفاصيل المقالة