Dynamics analysis of spatial parallel robot with rigid and flexible links

Qingyun Zhang; Xinhua Zhao; Liang Liu; Tengda Dai; Qingyun Zhang; Xinhua Zhao; Liang Liu; Tengda Dai

doi:10.3934/mbe.2020365

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 6: 7101-7129. doi: 10.3934/mbe.2020365

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Research article

Dynamics analysis of spatial parallel robot with rigid and flexible links

1.
School of Computer Science and Engineering, Tianjin University of Technology, Tianjin 300384, China
2.
Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, National Demonstration Center for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, Tianjin 300384, China

Received: 06 August 2020 Accepted: 09 October 2020 Published: 20 October 2020

To analyze the rigid–flexible coupling effects on the dynamic performance of a robot system, a dynamic model of a parallel robot with flexible spatial links is derived in detail using a floating frame of reference (FFR) formulation. Compared to the previous rigid–flexible coupling model where the kinematic chains are all flexible links or where the joints are all flexible components, the inertia matrix and the stiffness matrix are not constant matrix which leading to the differences in respect of dynamic performance in model. To verify the correctness of the derived dynamics equations, the dynamics solutions of the spatial parallel robot from an ideal rigid–body model and the FFR model containing rigid and flexible coordinates were established by an FFR formulation. Furthermore, a finite element analysis (FEA) model, which included rigid links and flexible spatial links, was constructed for comparison. The comparison of the three models showed that the trajectory trends were the same, but the motion trajectories of the end-effector obtained by the FFR and FEA models varied within a certain range, and the maximum variations occurred at the peaks of the trajectories. However, since the FFR model considered the coupling effects of rigid and flexible links and the micro-displacement of the end-effector, the amount of deformation was the largest.
- rigid–flexible coupling,
- floating frame of reference,
- multibody systems,
- dynamics,
- spatial mechanism
Citation: Qingyun Zhang, Xinhua Zhao, Liang Liu, Tengda Dai. Dynamics analysis of spatial parallel robot with rigid and flexible links[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 7101-7129. doi: 10.3934/mbe.2020365

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Abstract

To analyze the rigid–flexible coupling effects on the dynamic performance of a robot system, a dynamic model of a parallel robot with flexible spatial links is derived in detail using a floating frame of reference (FFR) formulation. Compared to the previous rigid–flexible coupling model where the kinematic chains are all flexible links or where the joints are all flexible components, the inertia matrix and the stiffness matrix are not constant matrix which leading to the differences in respect of dynamic performance in model. To verify the correctness of the derived dynamics equations, the dynamics solutions of the spatial parallel robot from an ideal rigid–body model and the FFR model containing rigid and flexible coordinates were established by an FFR formulation. Furthermore, a finite element analysis (FEA) model, which included rigid links and flexible spatial links, was constructed for comparison. The comparison of the three models showed that the trajectory trends were the same, but the motion trajectories of the end-effector obtained by the FFR and FEA models varied within a certain range, and the maximum variations occurred at the peaks of the trajectories. However, since the FFR model considered the coupling effects of rigid and flexible links and the micro-displacement of the end-effector, the amount of deformation was the largest.

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