چكيده به لاتين
Cooperative manipulators with closed kinematic chain are of great importance due to performing special missions such as displacement of large or heavy objects, assembling or forming parts and etc. In this paper, dynamic model of r cooperative manipulators withn_m flexible links derived by using recursive Gibbs-Appell formulation. Object grasped fully constrained by the manipulator’s end effector and manipulators transport the object simultaneously. The flexible links are modeled based on the assumed modes method along with the Euler-Bernoulli beam theory assumption. For computing the system equations, first the object and manipulators dynamic equations developed independently. Therefore, by preparing the constraint equations, the end effectors and object inter connection forces and torques omitted for the constrained equations. By arranging these equations, the final form of motion equations in joint space evaluated. In this regard, the manipulator’s Jacobian matrix is evaluated by tacking the effects of flexible links into accounts. Next, the forward dynamic equations simulated by MATLAB software and the simulation results have been compared with the equivalent system with rigid links and a similar mechanism in ANSYS Workbench. For inverse dynamic solution, with considering the joints redundancy, two restriction solutions selected among appropriated one. In the first case, the solution chosen by considering the force extracted on the object by the manipulators. While, the force only cause the object manipulation and omitted the object internal forces and stresses. For the second one, the problem solved by considering the minimum consumption energy during the motion with assuming the arbitrary load distribution between manipulator’s joints (with considering the motor’s joint capacity). In addition, dynamic load carrying capacity of robot for these two methods has been determined and compared. Finally the H∞ control algorithm implemented the concluded dynamic equations for predefined path and the results were compared with the PD control algorithm outcomes
