Dynamics of a Flexible-Link Planar Parallel Manipulator in Cartesian Space

1994 ◽  
Author(s):  
Abbas Fattah ◽  
Arun K. Misra ◽  
Jorge Angeles
Keyword(s):  
Parallel Manipulator ◽  
High Speed ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Flexible Link ◽  
End Effector ◽  
Joint Torques ◽  
Flexible Links ◽  
Cartesian Space ◽  
Planar Parallel Manipulator

Abstract The subject of this paper is the modeling and simulation of a flexible-link planar parallel manipulator in Cartesian space. Given a desired end-effector motion, the inverse kinematics and inverse dynamics of a rigid-link model of the parallel manipulator is used to obtain actuated joint torques. The actual end-effector motion and vibration of the flexible links are obtained using simulation (direct dynamics) for the flexible-link manipulator. Finite elements are used to model the flexible links, while the Euler-Lagrange formulation is used to derive the equations of motion of the uncoupled links. The equations of motion of all the links are assembled to obtain the governing equations for the entire system. The methodology of the natural orthogonal complement, which has been previously applied to flexible-link systems with open-chain structures, is used here to eliminate the constraint forces. Finally, geometric nonlinearities in elastic deformations, which are very important in high-speed operations, are also considered.

Bond Graph Modeling and Simulating of 3 RPR Planar Parallel Manipulator

2014 ◽  
Author(s):  
Cheng Yin ◽  
Shengqi Jian ◽  
Md. Hassan Faghih ◽  
Md. Toufiqul Islam ◽  
Luc Rolland
Keyword(s):  
Parallel Manipulator ◽  
High Speed ◽  
Reference Frames ◽  
Bond Graph ◽  
Dynamics Simulation ◽  
Bond Graphs ◽  
End Effector ◽  
Planar Parallel Manipulator ◽  
Bond Graph Modeling ◽  
Graph System

A 3-RPR planar parallel robot is a kind of planar mechanisms, which can work at high speed, with high accuracy and high rigidity. In this paper, a multi-body bond graph system will be built for the 3-RPR planar parallel manipulator (PPM), along with 3 PID controllers which give commands to 3 DC motors respectively. The advantage of bond graphs is that they can integrate different types of dynamics systems, the manipulator, the control and the motor can be modelled and simulated altogether in the same process. Bond graph will be established for each rigid body with body-fixed coordinate’s reference frames, which are connected with parasitic elements (damping and compliance) to each other. The PID set-point signals are generated by the explicit inverse kinematic equations. The 3 prismatic lengths constitute the measured feedback signals. In order to make the end-effector reach the ideal position with target orientation, the three links should reach the target lengths simultaneously. In this study, the dynamics simulation of 3-RPR PPM is conducted after building the bond graph system. As the 3 motors are working simultaneously and independently, the end-effector will arrive to the expected position. Finally, the bond graph and control system are validated with the compiled results and 3D animation. Force plot and torque plot will be generated as dynamics performance. Moreover, kinematics of manipulators are also calculated using bond graph. Eventually, bond graphs are shown to be effective in solving not only dynamic but also kinematic problems.

Dynamic characteristics of a 3-RPR planar parallel manipulator with flexible intermediate links

Robotica ◽  
2014 ◽  
Vol 33 (9) ◽  
pp. 1909-1925 ◽  
Author(s):  
Amirhossein Eshaghiyeh Firoozabadi ◽  
Saeed Ebrahimi ◽  
Ghasem Amirian
Keyword(s):  
Boundary Conditions ◽  
Dynamic Modeling ◽  
Parallel Manipulator ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
End Effector ◽  
Assumed Mode Method ◽  
Planar Parallel Manipulator

SUMMARYThis paper presents the dynamic modeling of a 3-RPR planar parallel manipulator with three flexible intermediate links in order to investigate the effects of the intermediate links flexibility on the undesired vibrations of the end-effector. For this purpose, the intermediate links are modeled as Euler--Bernoulli beams with two types of fixed-pinned and fixed-free boundary conditions based on the assumed mode method (AMM). The equations of motion of the 3-RPR manipulator are formulated using the augmented Lagrange multipliers method in the form of differential algebraic equations (DAEs) by incorporating the elastic and rigid coordinates in the set of generalized coordinates. After defining the initial conditions and imposing external forces to the manipulator, the equations are then solved numerically using the Modified Extended Backward-Differentiation Formula Implicit (MEBDFI) approach. Comparison of the simulation results for two different boundary conditions shows clearly the effects of flexibility of the intermediate links on the vibration of the end-effector trajectory. Results of this work can be used for the dynamic modeling of other manipulators or to design a controller for reducing the undesired vibrations.

Modal Analysis of High-Speed Parallel Manipulator with Flexible Links

2016 ◽  
Vol 826 ◽  
pp. 8-14 ◽  
Author(s):  
Zheng Sheng Chen ◽  
Ming Liu ◽  
Min Xiu Kong ◽  
Chen Ji
Keyword(s):  
Modal Analysis ◽  
Parallel Manipulator ◽  
High Speed ◽  
Structural Model ◽  
Lagrange Equation ◽  
Flexible Link ◽  
Flexible Coupling ◽  
Flexible Links ◽  
Coupling Technique ◽  
Abaqus Model

The modal analysis was carried out to investigate the proposed improved curvature based finite element method (ICFE) for parallel manipulator with flexible links. The flexible link was discretizatied with ICFE first, and with the proposed rigid-flexible coupling technique, the flexible displacement of the moving platform and passive links was obtained, then through Lagrange equation, the structural model was derived. At last, to investigate the accuracy and efficiency of the ICFE and rigid-flexible coupling technique, modal analysis of ICFE model with different nodes and comparison studies with CFE and the ABAQUS model was carried out.

Exponentially Stable Tracking Control for Multijoint Flexible-Link Manipulators

1993 ◽  
Vol 115 (1) ◽  
pp. 53-59 ◽  
Author(s):  
B. Paden ◽  
D. Chen ◽  
R. Ledesma ◽  
E. Bayo
Keyword(s):  
Tracking Control ◽  
Inverse Dynamics ◽  
Control Law ◽  
Flexible Link ◽  
Positive Real ◽  
End Effector ◽  
Joint Torques ◽  
Passive Joint ◽  
Exponentially Stable ◽  
Control Stability

In this paper we describe a new tracking control law for multijoint flexible-link manipulators. The scheme is a synthesis of the inverse dynamics solution for flexible manipulators developed by Bayo at UCSB and tracking control theory for rigid-link manipulators put forth by Bayard, Wen and others. We show that passive joint controllers, together with the feedforward of nominal joint torques corresponding to a desired end-effector trajectory, results in exponentially stable tracking control. Stability is proved (local to the desired trajectory) for a large class of passive controllers which include proportional and derivative controllers, and lead compensators. The proof is based on a simple Lyapunov analysis and the Positive-Real lemma.

Integrated optimal design of a high-speed planar parallel manipulator

2018 ◽  
Vol 233 (9) ◽  
pp. 2976-2990 ◽  
Author(s):  
Zhengsheng Chen ◽  
Minxiu Kong
Keyword(s):  
Optimal Design ◽  
Parallel Manipulator ◽  
High Speed ◽  
Design Method ◽  
Tracking Error ◽  
Dimensional Synthesis ◽  
Tracking Accuracy ◽  
Nsga Ii ◽  
Parameters Tuning ◽  
Planar Parallel Manipulator

To obtain excellent comprehensive performances of the planar parallel manipulator for the high-speed application, an integrated optimal design method, which integrated dimensional synthesis, motors/reducers selection, and control parameters tuning, is proposed, and the 3RRR parallel manipulator was taken as the example. The kinematic and dynamic performances of condition number, velocity index, acceleration capability, and low-order frequency are taken into accounts for the dimensional synthesis. Then, to match motors/reducers parameters and keep an economical cost, the constraint equations and the parameters library are built, and the cost is chosen as one of the optimization objectives. Also, to get high tracking accuracy, the dynamic forward plus proportional–derivative control scheme is introduced, and the tracking error is chosen as one of the optimization objectives. Hence, the optimization model including dimensional synthesis, motors/reducers selection and controller parameters tuning is established, which is solved by the genetic algorithm II (NSGA-II). The result shows that comprehensive performances can be effectively promoted through the proposed integrated optimal design, and the prototype was constructed according to the Pareto-optimal front.

Singularity robust inverse dynamics of planar 2-RPR parallel manipulators

2004 ◽  
Vol 218 (7) ◽  
pp. 721-730 ◽  
Author(s):  
S Kemal Ider
Keyword(s):  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Full Rank ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
Dynamic Equations ◽  
Revolute Joints ◽  
Planar Parallel Manipulator ◽  
Pass Through ◽  
Full Utilization

In planar parallel robots, limitations occur in the functional workspace because of interference of the legs with each other and because of drive singularities where the actuators lose control of the moving platform and the actuator forces grow without bounds. A 2-RPR (revolute, prismatic, revolute joints) planar parallel manipulator with two legs that minimizes the interference of the mechanical components is considered. Avoidance of the drive singularities is in general not desirable since it reduces the functional workspace. An inverse dynamics algorithm with singularity robustness is formulated allowing full utilization of the workspace. It is shown that if the trajectory is planned to satisfy certain conditions related to the consistency of the dynamic equations, the manipulator can pass through the drive singularities while the actuator forces remain stable. Furthermore, for finding the actuator forces in the vicinity of the singular positions a full rank modification of the dynamic equations is developed. A deployment motion is analysed to illustrate the proposed approach.

Path Tracking of Parallel Manipulators in the Presence of Force Singularity

2005 ◽  
Vol 127 (4) ◽  
pp. 550-563 ◽  
Author(s):  
C. K. Kevin Jui ◽  
Qiao Sun
Keyword(s):  
Motion Planning ◽  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Parallel Manipulators ◽  
Path Tracking ◽  
Singularity Avoidance ◽  
Design Complexity ◽  
Actuation Redundancy ◽  
Planar Parallel Manipulator ◽  
Simulation Results

Parallel manipulators are uncontrollable at force singularities due to the infeasibly high actuator forces required. Existing remedies include the application of actuation redundancy and motion planning for singularity avoidance. While actuation redundancy increases cost and design complexity, singularity avoidance reduces the effective workspace of a parallel manipulator. This article presents a path tracking type of approach to operate parallel manipulators when passing through force singularities. We study motion feasibility in the neighborhood of singularity and conclude that a parallel manipulator may track a path through singular poses if its velocity and acceleration are properly constrained. Techniques for path verification and tracking are presented, and an inverse dynamics algorithm that takes actuator bounds into account is examined. Simulation results for a planar parallel manipulator are given to demonstrate the details of this approach.

Analysis and Validation of a Flexible Planar Two Degrees-of-Freedom Parallel Manipulator With Structural Passive Compliance

2019 ◽  
Vol 12 (1) ◽  
Author(s):  
Genliang Chen ◽  
Zhuang Zhang ◽  
Lingyu Kong ◽  
Hao Wang
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Interaction Force ◽  
Flexible Manipulator ◽  
End Effector ◽  
Flexible Links ◽  
Wide Range ◽  
Pick And Place ◽  
Passive Compliance ◽  
Large Deflection Problem

Abstract Passive compliance plays an important role in robot pick-and-place manipulation where large interaction force will be produced in response to small misalignments. In this paper, the authors report on compliance analysis and validation of a novel planar pick-and-place parallel manipulator consisting of a flexible limb. In the proposed manipulator, a planar flexible parallelogram linkage, which is coupled with a rigid one, is introduced to connect the moving and the base platforms. Since the flexible parallelogram linkage is capable of producing large deformation in both the horizontal and the vertical directions, the end effector of the manipulator can generate wide-range motions because of the flexible links. An efficient approach to the large deflection problem of flexible links is used to precisely predict the kinetostatics of the manipulator. Then, a compensation algorithm to the structural deflection of the links can be developed to actively control the position of the parallel manipulator’s end effector. The merit of the proposed flexible manipulator is its intrinsic passive compliance while performing pick-and-place tasks. A prototype is fabricated to conduct experiments for the validation of the proposed idea. The results show that the prototype has acceptable positioning accuracy, even when a large external load is exerted on its end effector. The compliance properties of the proposed flexible manipulator have also been verified in both the horizontal and the vertical directions.

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