Integrating Dynamics into Design and Motion Optimization of a 3-PRR Planar Parallel Manipulator with Discrete Time Transfer Matrix Method

Abstract

This paper presents a novel method of dynamic modeling and design optimization integrated with dynamics for parallel robot manipulators. Firstly, a computationally efficient modeling method, the discrete time transfer matrix method (DT-TMM), is proposed to establish the dynamic model of a 3-PRR planar parallel manipulator (PPM) for the first time. The numerical simulations are performed with both the proposed DT-TMM dynamic modeling and the ADAMS modeling. The applicability and effectiveness of DT-TMM in parallel manipulators are verified by comparing the numerical results. Secondly, the design parameters of the 3-PRR parallel manipulator are optimized using the kinematic performance indices, such as global workspace conditioning index (GWCI), global condition index (GCI), and global gradient index (GGI). Finally, a dynamic performance index, namely, driving force index (DFI), is proposed based on the established dynamic model. The described motion trajectory of the moving platform is placed into the optimized workspace and the initial position is determined to finalize the end-effector trajectory of the parallel manipulator by the further optimization with the integrated kinematic and dynamic performance indices. The novelty of this work includes (1) developing a new dynamic model method with high computation efficiency for parallel robot manipulators using DT-TMM and (2) proposing a new dynamic performance index and integrating the dynamic index into the motion and design optimization of parallel robot manipulators.

A critical review of modelling methods for flexible and rigid link manipulators

“…The LPM also does not develop sufficiently accurate dynamic model especially for less number of lumped masses and need to increase the number of lumped masses to represent the system well which imposes the difficulty of the modelling process. Even the Lagrangian [120,122,123,127,144,146,147] RLM Lagrange's equation [148][149][150][151][152][153][154][155][156] Newtonian method [150,151,[157][158][159][160] Kinematic method [149,157,158,[161][162][163][164][165][166][167] method is easy and appropriate for obtaining the equations of motion of FLMs, it is essential to use an approximation method to express the deflection of FLMs. Modelling RLMs is much easier than modelling FLMs as RLMs do not have any deflection or error on the manipulator's tip caused by the flexibility of the links.…”

Vibration Modeling and Analysis of a Flexible 3-PRR Planar Parallel Manipulator Based on Transfer Matrix Method for Multibody System

“…It consists of a regular triangle mobile platform C 1 C 2 C 3 , with three closed branch chains connected to the fixed base platform A 1 A 2 A 3 . Each branch chain has an active moving joint and two passive rotating joints that move along the straight line of the guideway [30,31]. The global coordinate system OXY is set at the position of the base platform A 1 , and the initial angle of the mobile platform is expressed as ϕ.…”

“…Each chain system consists of a flexible link, a slider, and two smooth hinges. Three The state vector form of the planar hinge can be defined in a similar manner to Equations ( 4) and ( 5), and then from the literature [31], the transfer equation of the smooth hinge can be obtained as:…”

Efficient technique in computational dynamic modeling of a flexible manipulator with large deformation

“…The extolling virtues of the DT-TMM have brought about the use of this method in kinematic and dynamic analysis and the optimization of rigid parallel manipulators such as Stewart platform (Jiang et al, 2020(Jiang et al, , 2021 and a planar 3-PRR manipulator (Si et al, 2020). After when the DT-TMM was used to examine the small deformation of a single flexible link manipulator under feedback control (Krauss and Okasha, 2013), the acceleration-based DT-TMM was proposed for flexible link manipulators (Zhang et al, 2018).…”