Two-time scale controller design for a high speed planar parallel manipulator with structural flexibility

Robotica ◽  
2002 ◽  
Vol 20 (5) ◽  
pp. 519-528
Author(s):  
Bongsoo Kang ◽  
Benny Yeung ◽  
James K. Mills
Keyword(s):  
Time Scale ◽  
Parallel Manipulator ◽  
High Speed ◽  
Parallel Manipulators ◽  
Structural Vibration ◽  
Scale Model ◽  
Fast Time ◽  
Inertial Forces ◽  
Linear Quadratic ◽  
Planar Parallel Manipulator

SummaryPlanar parallel manipulators, with potential applications in high speed, high acceleration tasks such as electronic component placement, would be subject to mechanical vibration due to high inertial forces acting on the linkages and other components. To achieve high throughput capability, such motion induced vibration would have to be damped quickly, to reduce settling time of the platform position and orientation. This paper develops a two-time scale dynamic model of a three-degree-of-freedom planar parallel manipulator with structurally flexible linkages. Based on the two-time scale model, a composite controller, consisting of a computed torque controller for the slow time-scale or rigid body subsystem dynamics, and a linear-quadratic state-feedback regulator for the fast time-scale flexible dynamic subsystem, is designed. Simulation results show that the composite control scheme permits the parallel manipulator platform to follow a given desired trajectory, while damping structural vibration arising due to excitation from inertial forces.

Investigation of axial forces on dynamic properties of a flexible 3-PRR planar parallel manipulator moving with high speed

Robotica ◽  
2009 ◽  
Vol 28 (4) ◽  
pp. 607-619 ◽  
Author(s):  
Xuping Zhang ◽  
James K. Mills ◽  
William L. Cleghorn
Keyword(s):  
Parallel Manipulator ◽  
High Speed ◽  
Dynamic Properties ◽  
Parallel Manipulators ◽  
Body Motion ◽  
Valuable Insight ◽  
Bending Vibration ◽  
Assumed Mode Method ◽  
Axial Forces ◽  
Planar Parallel Manipulator

SUMMARYThe effect of axial forces on the dynamic properties is formulated and investigated for a 3-PRR planar parallel manipulator with three flexible intermediate links. A dynamic model of the manipulator system is developed based on the assumed mode method with the consideration of the effect of longitudinal forces on lateral stiffness is included. The flexible intermediate links are modeled as Euler–Bernoulli beams with pinned-pinned boundary conditions, which are verified by experimental modal tests. Natural frequencies of bending vibration of the intermediate links are derived as the functions of axial force and rigid-body motion of the manipulator. Dynamic behavior including the effect of axial forces on lateral deformation is investigated, and configuration-dependant frequencies are analyzed. Numerical simulations of configuration-dependent frequency properties and axial forces are performed to illustrate the effect of axial forces on the dynamic behaviors of the flexible parallel manipulator. Simulation results of mode amplitudes, deformations, axial forces, inertial, and coupling forces are presented, and further validate the theoretical derivations. These analyses and results provide a new and valuable insight to the design and control of the parallel manipulators with flexible intermediate links.

Effect of links deformation on motion precision of parallel manipulator based on flexible dynamics

2017 ◽  
Vol 44 (6) ◽  
pp. 776-787 ◽  
Author(s):  
Chunxia Zhu ◽  
Jay Katupitiya ◽  
Jing Wang
Keyword(s):  
Parallel Manipulator ◽  
High Speed ◽  
Beam Theory ◽  
Parallel Manipulators ◽  
Dynamic Responses ◽  
Axial Deformation ◽  
Content Type ◽  
High Performing ◽  
Coupling Equations ◽  
The Relationship

Purpose Manipulator motion accuracy is a fundamental requirement for precision manufacturing equipment. Light weight manipulators in high speed motions are vulnerable to deformations. The purpose of this work is to analyze the effect of link deformation on the motion precision of parallel manipulators. Design/methodology/approach The flexible dynamics model of the links is first established by applying the Euler–Bernoulli beam theory and the assumed modal method. The rigid-flexible coupling equations of the parallel mechanism are further derived by using the Lagrange multiplier approach. The elastic energy resulting from spiral motion and link deformations are computed and analyzed. Motion errors of the 3-link torque-prismatic-torque parallel manipulator are then evaluated based on its inverse kinematics. The validation experiments are also conducted to verify the numerical results. Findings The lateral deformation and axial deformation are largest at the middle of the driven links. The axial deformation at the middle of the driven link is approximately one-tenth of the transversal deformation. However, the elastic potential energy of the transversal deformation is much smaller than the elastic force generated from axial deformation. Practical implications Knowledge on the relationship between link deformation and motion precision is useful in the design of parallel manipulators for high performing dynamic responses. Originality/value This work establishes the relationship between motion precision and the amount of link deformation in parallel manipulators.

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.

scholarly journals Workspace Delineation of Cable-Actuated Parallel Manipulators

2004 ◽  
Author(s):  
Ethan Stump ◽  
Vijay Kumar
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Extensive Literature ◽  
Reachable Workspace ◽  
Planar Parallel Manipulator ◽  
Analytic Expressions

While there is extensive literature available on parallel manipulators in general, there has been much less attention given to cable-driven parallel manipulators. In this paper, we address the problem of analyzing the reachable workspace using the tools of semi-definite programming. We build on earlier work [1, 2] done using similar techniques by deriving limiting conditions that allow us to compute analytic expressions for the boundary of the reachable workspace. We illustrate this computation for a planar parallel manipulator with four actuators.

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.

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