Recursive Kinematics and Inverse Dynamics for a Planar 3R Parallel Manipulator

We focus on the development of modular and recursive formulations for the inverse dynamics of parallel architecture manipulators in this paper. The modular formulation of mathematical models is attractive especially when existing sub-models may be assembled to create different topologies, e.g., cooperative robotic systems. Recursive algorithms are desirable from the viewpoint of simplicity and uniformity of computation. However, the prominent features of parallel architecture manipulators-the multiple closed kinematic loops, varying locations of actuation together with mixtures of active and passive joints-have traditionally hindered the formulation of modular and recursive algorithms. In this paper, the concept of the decoupled natural orthogonal complement (DeNOC) is combined with the spatial parallelism of the robots of interest to develop an inverse dynamics algorithm which is both recursive and modular. The various formulation stages in this process are highlighted using the illustrative example of a 3R Planar Parallel Manipulator.

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Inverse dynamics of a 3-prismatic—revolute—revolute planar parallel manipulator using natural orthogonal complement

Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering ◽

10.1243/09596518jsce1098 ◽

2011 ◽

Vol 225 (2) ◽

pp. 258-269 ◽

Cited By ~ 2

Author(s):

H Kordjazi ◽

A Akbarzadeh

Keyword(s):

Parallel Manipulator ◽

Inverse Dynamics ◽

Orthogonal Complement ◽

Planar Parallel Manipulator

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Singularity robust inverse dynamics of planar 2-RPR parallel manipulators

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/0954406041319527 ◽

2004 ◽

Vol 218 (7) ◽

pp. 721-730 ◽

Cited By ~ 13

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.

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Path Tracking of Parallel Manipulators in the Presence of Force Singularity

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2098893 ◽

2005 ◽

Vol 127 (4) ◽

pp. 550-563 ◽

Cited By ~ 24

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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Recursive Kinematics and Inverse Dynamics for Parallel Manipulators

Dynamic Systems and Control, Volumes 1 and 2 ◽

10.1115/imece2003-42868 ◽

2003 ◽

Author(s):

Waseem A. Khan ◽

Venkat N. Krovi ◽

Subir K. Saha ◽

Jorge Angeles

Keyword(s):

Inverse Dynamics ◽

Parallel Architecture ◽

Parallel Manipulators ◽

Orthogonal Complement ◽

Recursive Formulation

We examine here the modular and recursive formulation of the inverse dynamics of parallel architecture mainpulators. The concept of the decoupled natural orthogonal complement (DeNOC) is combined with the spatial parallelism of the robots of interest to develop an inverse dynamics algorithm which is both recursive and modular.

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Performance Evaluation of a 2-DOF Planar Parallel Manipulator

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.121-126.2829 ◽

2011 ◽

Vol 121-126 ◽

pp. 2829-2833

Author(s):

Xiao Rong Zhu ◽

Hui Ping Shen

Keyword(s):

Machine Tools ◽

Parallel Manipulator ◽

Inverse Dynamics ◽

Forward Kinematics ◽

Planar Parallel Manipulator ◽

Velocity Equation ◽

Force Transmissibility ◽

Inverse Dynamics Problem ◽

Linear Actuators ◽

Mobile Base

In this paper, a 2-DOF planar parallel manipulator actuated horizontally by linear actuators is proposed. The inverse and forward kinematics can be described in closed form. The velocity equation, singularity of the manipulator and the conditioning index is investigated. In addition, the inverse dynamics problem of the device is investigated employing the Lagrange approach. The dynamic simulation is carried out. The results show that the kinematics performance and the force transmissibility are worse when the end-effecter moves near the singularity. The proposed manipulator can be applied to the field of machine tools or used as the mobile base for a spatial manipulator. The results of the paper are very useful for the design and application of the new manipulator.

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

20th Design Automation Conference: Volume 2 — Robust Design Applications; Decomposition and Design Optimization; Optimization Tools and Applications ◽

10.1115/detc1994-0160 ◽

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.

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The Dynamic Analysis of a 2-PRR Planar Parallel Mechanism

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/095440605x31832 ◽

2005 ◽

Vol 219 (9) ◽

pp. 901-909 ◽

Cited By ~ 2

Author(s):

L-P Wang ◽

J-S Wang ◽

J Chen

Keyword(s):

Parallel Mechanism ◽

Parallel Manipulator ◽

Degrees Of Freedom ◽

Inverse Dynamics ◽

Driving Forces ◽

Inverse Dynamic ◽

Inverse Dynamic Model ◽

Planar Parallel Manipulator ◽

Euler Approach ◽

Motion Parameters

The article presents the inverse dynamics of a two-degrees-of-freedom planar parallel manipulator by the Newton-Euler approach. On the basis of the inverse dynamic model, the driving forces of actuators are simulated in different motion parameters. Further, the effects of inertia of each moving component to the driving forces are computed through the numerical method.

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