Stiffness Characteristics Analysis of a Novel 3- DOF Parallel Kinematic Machine Tool

Abstract

A novel 1T2R with three degrees of freedom redundantly actuated and overconstrained 2RPU-2SPR parallel manipulator is here presented as an alternative approach for high speed machining in aerospace field.  Firstly, the actuation and constraints of the parallel manipulator imposed by passive joints are analyzed in terms of the screw theory, and the degree of freedom of the parallel manipulator is further derived. Secondly, the kinematic analysis is carried out, the inverse position and geometric constraint equations of the parallel manipulator are established, and the overall Jacobian matrix was explicitly derived. Subsequently, the stiffness matrix of the chain is deduced considering the elastic deformation of the link, and the stiffness matrix of the parallel manipulator is established by the differential mapping relationship between the actuated chains and the moving platform. The linear and angular stiffness, eigenscrew decomposition, and maximum and minimum stiffness eigenvalues are introduced to evaluate the stiffness characteristics of the manipulator. Finally, through some numerical examples, distributions law of the performance indices of redundantly actuated and overconstrained 2-RPU-2SPR parallel manipulator are illustrated in details. The results demonstrate that the three degree of freedom redundant actuation parallel manipulator proposed in this paper has much better stiffness performance than the 2-RPU-SPR parallel manipulator, and has much more extensive prospect in engineering applications.

Trajectory Tracking Control Study of a New Parallel Mechanism with Redundant Actuation

“…For modeling purposes, as shown in Figure 2, we assume a fixed coordinate system B-xyz at the centered point B of the fixed platform and a moving coordinate system A-uvw on the square moving platform at the centered point A, along with the z-axis and w-axis perpendicular to the platform, and the x-axis and y-axis parallel to the u-axis and v-axis, respec- International Journal of Aerospace Engineering squares so as to yield a symmetric architecture of the parallel mechanism. With these geometric conditions satisfied, the moving platform of parallel mechanism will pose with three independent degrees of freedom in the Cartesian space by controlling the movement of four servo actuators, that is, two rotational degrees of freedom around the x-axis and v-axis and one translational degree of freedom along the z-axis; in this case, the spatial rotations are coupled with the change of four nonidentical limbs [30]. What is more, as the number of actuated joints is greater than that of the degree of freedom, it belongs to a redundantly actuated parallel mechanism.…”

Kinematic analysis of overconstrained manipulators with partial subspaces using decomposition method

“…Yang et al [26] proposed a modeling method for the elastostatic stiffness of OPMs using screw theory and applying the method to 2UPR-RPU PMs. Zhang and Fang [27] proposed a 1T2R OPM with 2RPU-2SPR joint configuration and they calculated the linear and angular stiffness of the PM to find distributions law of the performance indices of redundantly actuated and overconstrained. Li et al [28] proposed a method for the analytical elastostatic stiffness modeling of OPMs.…”

The Dexterity Analysis of a Spatial Three-Degree of Freedom Parallel Manipulator with Constrained Branch

“…In recent years, the 1T2R parallel manipulator has attracted increasing attentions in both academia and industry. The research focus is mainly on the configuration synthesis, kinematics and dynamics performance analysis and dimension evaluation [11], [12]. In the configuration synthesis, there exists a class of mechanism composed of suitable constrained branch and unconstrained active branches, such as Tricept [13].…”