Kinematics, force and stiffness analyses of parallel manipulators

Parallel manipulators are closed-loop mechanisms which are widely used in the industry, e.g., in aerospace industry as flight simulators because of high acceleration (dynamic) characteristics, automotive or entertainment industries due to their advantages of having good load carrying capacity and high precision of their mobile platform (end effector). In this study, kinematic and force analyses of parallel manipulators, which would provide useful information about the motion and force capabilities of these manipulators, are investigated. The stiffness analysis of closed-loop mechanisms is formulated to estimate the elastic properties in the task space. A class of closed-loop mechanisms is the wire-actuated parallel manipulators. These manipulators use wires, which are tension only members, as actuation units. Force-closure conditions for the wire-actuated parallel manipulators are studied to ensure that wire-actuated parallel manipulators can operate under any loading conditions.; Position and first and second order kinematics of closed-loop mechanisms are formulated. The transfer of first and second order kinematic variables, i.e., joint velocities and accelerations, between the minimum number of coordinates to express he manipulator kinematics (generalized coordinates), passive coordinates and the end effector coordinates is provided.; A formulation of force analysis, which includes the calculation of the reaction forces of closed-loop mechanisms, is given. Flexibility properties of the manipulators are incorporated in case the manipulator is overdetermined. Thus, it becomes possible to find the driving torques and reaction forces for given end effector forces.; For wire-actuated parallel manipulators, force-closure conditions are studied to check that the wires used in the wire-actuated parallel manipulators are able to exert and withstand forces during the interaction of the mobile platform with the environment. Thus, for given wire attachment points of a wire-actuated parallel manipulator, the force-closure conditions are checked to test its manipulability properties. This procedure is used for the synthesis of the wire-actuated parallel manipulators.; Stiffness analysis of parallel manipulators with respect to a fixed Cartesian coordinate system is performed. An asymmetric stiffness matrix, which includes the contribution of the external loading, gravity forces, stiffness of passive and active joints and stiffness of wire (if wires are used for actuation) is obtained. Stiffness and stability characteristics of parallel manipulators are studied via eigenvalue problems. Weighted eigenvalue problems are discussed and compliant axes, centre of elasticity, centre of stiffness properties of robotic manipulators are illustrated.; The theory developed in this study is implemented on a three degrees of freedom planar parallel manipulator and a four degrees of freedom wire-actuated parallel manipulator. Sample results are illustrated and discussions are given.