Closed-form dynamic modeling and performance analysis of an over-constrained 2PUR-PSR parallel manipulator with parasitic motions

Mathematical and Computer Modelling of Dynamical Systems

et al. 2021

This research presents the mathematical modelling of kinematic and complete dynamic analysis of a novel over-constrained parallel mechanism, which consists of two universal-prismatic-revolute joint limbs and one revolute-revolute-universal joint limb. The kinematic model is constructed based on the closed-loop vector method and the velocity Jacobian matrix is deduced, velocitymapping relationships between all moving components and moving platform are also performed. Afterwards, inertia and applied forces are analysed, the complete dynamic equations with the classical Stribeck friction model of the proposed structure is established based on the principle of virtual work. A theoretical numerical example is given to solve kinematics and dynamics solutions, and theoretical forces from developed dynamic formulation are verified by the physic model simulation in Simscape and the rigidflexible coupling model simulation in Adams. A good agreement between the theoretical results and multi-body software simulation is found.

“…Substituting Equation (17) into Equation ( 23), the angular velocity of UPR limb can be derived as…”

Section: Velocity Analysis Of Limbsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of an over-constrained parallel mechanism with the principle of virtual work

Miao

Mathematical and Computer Modelling of Dynamical Systems

et al. 2021

“…Compared with serial manipulators, PMs with closed kinematic structures perform well in terms of accuracy, rigidity, and payload capacity and show high potentials to deal with numerous tasks [1][2][3]. erefore, the detailed analyses of PMs are extremely important, including the workspace [4], kinematics [5], dynamics [6], elastostatics [7], and motion/force transmissibility [8].…”

Section: Introductionmentioning

confidence: 99%

Elastostatic Stiffness Analysis for the US/UPS Parallel Manipulators

Mathematical Problems in Engineering

Yang

2020

Self Cite

The virtual joint method (VJM) cannot calculate the strain energy stored in each rod. In order to solve the problem, a modeling method of the elastostatic stiffness was investigated for the UP/UPS parallel manipulators (PMs), taking the example of the 6-SPS PM. The modeling method was based on screw theory, Castigliano’s theorem, and strain energy (where U, P, and S, respectively, denote universal, prismatic, and spherical joints). First, the actuator and constraint wrenches of the mechanism were obtained by screw theory. Second, compact limb stiffness matrices were obtained in terms of strain energy and Castigliano’s second theorem. Finally, analytic expressions for the overall stiffness matrix of the mechanism and the amplitudes of the actuator force were obtained by adopting the virtual work principle and the balance equation for the mobile platform. All relative errors between the results of the analytical model and the finite element model are below 2%, which validates the effectiveness of the elastostatic stiffness model. The virtual work index was adopted to evaluate the stiffness performance of the mechanism, and the results show that the stiffness is not only related to position and orientation but also closely related to the directions of external loads. It is also demonstrated that the method has general adaptability for the stiffness analysis for the US/UPS PMs, laying the foundation for further reasonable dynamic design and optimization of such manipulators.

“…4 Unlike serial manipulators, an explicit dynamic formulation of the SPM is much more complicated due to the closed kinematic chain. The literature on dynamic modeling of PMs mainly falls into four categories: Euler–Lagrange formulation, 5,6 Newton–Euler laws, 8,9 Kane method, 10–12 the principle of virtual work, 13–16 and Gibbs–Appell equations. 17,18…”

Section: Introductionmentioning

confidence: 99%

“…Chen et al. 8 presented a systematic dynamic modeling and performance analysis method of an overconstrained 2PUR-PSR parallel manipulator with parasitic motions. However, the Newton–Euler approach usually results in a set of differential algebraic equations with the maximum number of coordinates.…”

Section: Introductionmentioning

confidence: 99%

An efficient method for the dynamic modeling and analysis of Stewart parallel manipulator based on the screw theory

Hou

Proceedings of the Institution of Mechanical Engineers, Part C:

Zeng

2019

Dynamic modeling serves as the fundamental basis for dynamic performance analysis and is an essential aspect of the control scheme design of parallel manipulators. This report presents a concise and efficient solution to the dynamics of Stewart parallel manipulators based on the screw theory. The initial pose of these manipulators is described. Then the pose matrix of each link of the Stewart parallel mechanism is obtained using an inverse kinematics solution and an exponential product formula. Considering the constraint relationship between joints, the constraint matrix of the Stewart parallel manipulator is deduced. In addition, the Jacobian matrix and the twist of each link are obtained. Moreover, by deriving the differential form of the constraint matrix, the spatial acceleration of each link is obtained. Based on the force balance relationship of each link, the inverse dynamics and the general form of the dynamic model of the Stewart parallel manipulator is established and the process of inverse dynamics is summarized. The dynamic model is then verified via dynamic simulation using the ADAMS software. A numerical example is considered to demonstrate the feasibility and effectiveness of this model. The proposed dynamic modeling approach serves as a fundamental basis for structural optimization and control scheme design of the Stewart parallel manipulators.