Abstract
This paper presents the methods of structural-parametric synthesis and kinematic analysis of a parallel manipulator with three degrees of freedom working in a cylindrical coordinate system. This parallel manipulator belongs to a RoboMech class because it works under the set laws of motions of the end-effector and actuators, which simplifies the control system and improves its dynamics. Parallel manipulators of a RoboMech class work with certain structural schemes and geometrical parameters of their links. The considered parallel manipulator is formed by connecting the output point to a base using one passive and two active closing kinematic chains (CKC). Passive CKC have zero degree of freedom and it does not impose a geometrical constraint on the movement of the output point, so the geometrical parameters of the links of the passive CKC are freely varied. Active CKCs have active kinematic pairs and they impose geometrical constraints on the movement of the output point. The geometrical parameters of the links of the active CKCs are determined on the basis of the approximation problems of the Chebyshev and least-square approximations. For this, the equations of geometrical constraints are derived in the forms of functions of weighted differences, which are presented in the forms of generalized (Chebyshev) polynomials. This leads to linear iterative problems. The direct and inverse problems of the kinematics of the investigated parallel manipulator are solved. In the direct kinematics problem, the coordinates of the output point are determined by the given position of the input links. In the inverse kinematics problem, the positions of the input links are determined by the coordinates of the output point. The direct and inverse problems of the kinematics of the investigated parallel manipulator are reduced to solving problems on the positions of Sylvester dyads. Numerical results of structural-parametric synthesis and kinematic analysis of the considered parallel manipulator are presented. The numerical results of the kinematic analysis show that the maximum deviation of the movement of the output point from the orthogonal trajectories is 1.65 %
Highlights
Existing methods of designing both serial and parallel manipulating robots are mainly reduced to solving the inverse kinematics problem, i. e. determining the laws of movements of manipulator actuators according to the specified laws of movements of end-effectors, followed by the development of control systems
The basis for the structural synthesis of planar mechanisms is proposed in Assur [4, 5], according to which the mechanism is formed by connecting to the input link and the base of structural groups with zero degree of freedom (DOF)
According to the developed principle of the formation of mechanisms and manipulators [1], this parallel manipulator is formed by connecting the output object to the base using three closing kinematic chains (CKC): one passive ABP and two active CDE and FGH in the following sequence: firstly, the point P is connected to the base using the passive СKC АВР, reaching all the specified positions of the point P along the OX and OY axes, we connect the active CKC CDE whose active kinematic pair C reproduces the coordinates YPj along the vertical lines, lastly, we connect the active CKC FGH, whose active kinematic pair F reproduces the coordinates XPi along the horizontal lines
Summary
Existing methods of designing both serial and parallel manipulating robots are mainly reduced to solving the inverse kinematics problem, i. e. determining the laws of movements of manipulator actuators according to the specified laws of movements of end-effectors, followed by the development of control systems. E. determining the laws of movements of manipulator actuators according to the specified laws of movements of end-effectors, followed by the development of control systems. Mechanisms, as well as manipulating robots, are designed to move end-effectors according to the specified laws of movements. Setting the laws of movements of the actuators of the designed manipulators, along with the specified laws of movements of the end-effectors, improves their dynamics and increases efficiency. E. manipulators with closed kinematic chains, which possess the property of manipulating robots as the manipulation of moving output objects in accordance with their laws of movements and possess the property of mechanisms as setting the laws of movements of actuators, are called parallel manipulators of a RoboMech class [1,2,3]. In simultaneously setting the laws of movement of end-effectors and actuators, parallel manipulators of a RoboMech class work under certain structural schemes and geometric parameters of the links
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