It is known that a parallel manipulator at a singular configuration can gain one or more degrees of freedom and become uncontrollable, that is, it might not reproduce a stable motion along a prescribed trajectory. However, it is proved experimentally that there is possible passing through the singular zones. This was simulated and shown through numerical examples and illustrated on several parallel structures. In this paper, we determine the optimal dynamic conditions generating a stable motion inside the singular zones. The obtained results show that the general condition for passing through a singularity can be defined as follows: the end-effector of the parallel manipulator can pass through the singular positions without perturbation of motion if the wrench applied on the end-effector by the legs and external efforts of the manipulator are orthogonal to the twist along the direction of the uncontrollable motion. This condition is obtained from the tion of the uncontrollable motion. This condition is obtained from the inverse dynamics and analytically demonstrated by the study of the Lagrangian of a general parallel manipulator. Numerical simulations are carried out using the software ADAMS and validated through experimental tests.
This paper is focused on the study of singularity of planar parallel manipulators taking into account the force transmission, i.e. study of singularity of planar manipulator by introducing the force transmission factor. Thus the singularity zones in the workspace of the manipulator are defined not only by kinematic criterions from the theoretical perfect model of the manipulator but also by the quality of force transmission. For this purpose, the pressure angle is used as an indicator of force transmission. The optimal control of the pressure angle for a given trajectory of the manipulator is realized by means of legs with variable structure. The suggested procedure to determination of the optimal structure of the planar parallel manipulator 3-RPR is illustrated by two numerical simulations.
This paper deals with the solutions of the problem of the shaking force and shaking moment balancing of planar mechanisms by different methods based on the generation of the movements of counterweights. Some special cases are examined, such as balancing methods based on the copying properties of pantograph systems that carry the counterweights (formed by gears or by toothed-belt transmissions). The pantograph system executes a movement exactly opposite to the movement of the total center of the movable link masses. Such a solution provides the conditions for dynamic balancing with a relatively small increase of the total mass of the movable links. The methods are illustrated by many examples.
This paper proposes a new solution to the problem of torque minimization of spatial parallel manipulators. The suggested approach involves connecting a secondary mechanical system to the initial structure, which generates a vertical force applied to the manipulator platform. Two versions of the added force are considered: constant and variable. The conditions for optimization are formulated by the minimization of the root-mean-square values of the input torques. The positioning errors of the unbalanced and balanced parallel manipulators are provided. It is shown that the elastic deformations of the manipulator structure which are due to the payload, change the altitude and the inclination of the platform. A significant reduction of these errors is achieved by using the balancing mechanism. The efficiency of the suggested solution is illustrated by numerical simulations and experimental verifications. The prototype of the suggested balancing mechanism for the Delta robot is also presented.
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