Performance Evaluation of a 2-DOF Planar Parallel Manipulator

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.

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.

A Novel Parallel Mechanism With 3-RRUR Legs

2007 ◽  
Author(s):  
Yanwen Li ◽  
Yueyue Zhang ◽  
Lumin Wang ◽  
Zhen Huang
Keyword(s):  
Machine Tools ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Symmetrical Structure ◽  
Forward Kinematic ◽  
Accumulated Error

This paper investigates a novel 4-DOF 3-RRUR parallel manipulator, the number and the characteristics of its degrees of freedom are determined firstly, the rational input plan and the invert and forward kinematic solutions are carried out then. The corresponding numeral example of the forward kinematics is given. This type of parallel manipulators has a symmetrical structure, less accumulated error, and can be used to construct virtual-axis machine tools. The analysis in this paper will play an important role in promoting the application of such manipulators.

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

2004 ◽  
Vol 127 (4) ◽  
pp. 529-536 ◽  
Author(s):  
Waseem A. Khan ◽  
Venkat N. Krovi ◽  
Subir K. Saha ◽  
Jorge Angeles
Keyword(s):  
Mathematical Models ◽  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Parallel Architecture ◽  
Robotic Systems ◽  
Orthogonal Complement ◽  
Recursive Algorithms ◽  
Planar Parallel Manipulator ◽  
Kinematic Loops

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.

Kinematic Analysis of a Planar Mechanism Driven by Two Orthogonal Layout Actuators

2012 ◽  
Vol 490-495 ◽  
pp. 2305-2309
Author(s):  
Xiao Rong Zhu ◽  
Yi Lu ◽  
Hui Ping Shen
Keyword(s):  
Closed Form ◽  
Kinematic Analysis ◽  
Machine Tools ◽  
Jacobi Matrix ◽  
The Other ◽  
Stiffness Index ◽  
Forward Kinematics ◽  
Performance Indices ◽  
Hand Dexterity ◽  
Mobile Base

In this paper, a planar five-bar mechanism driven by two orthogonal layout actuators is proposed. The inverse and forward kinematics can be described in closed form. The Jacobi matrix, singularity and workspace of the mechanism are investigated. In addition, charts of some performance indices, such as dexterity, velocity, payload capability and stiffness index, are plotted. The results show that the mechanism has a flatter singularity-free workspace, which is usually our research object. On the other hand, Dexterity, Payload capability and stiffness index of the mechanism are basically the same distribution on the workspace, which are axis symmetric. But, the trend of velocity index is opposite. The proposed mechanism 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 mechanism

Optimal Kinematic Design of a 2-DOF Planar Parallel Manipulator

2010 ◽  
Vol 44-47 ◽  
pp. 1843-1847
Author(s):  
Xiao Rong Zhu ◽  
Hui Ping Shen ◽  
Wei Zhu
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Operating Mode ◽  
Performance Indices ◽  
Operating Modes ◽  
Geometry Design ◽  
Planar Parallel Manipulator ◽  
Inverse Solutions ◽  
Linear Actuators ◽  
Global And Local

This paper addresses geometry design and operating mode optimum design of a new kind of 2-DOF parallel manipulator actuated horizontally by linear actuators. The forward and inverse kinematics of this manipulator are derived. The four groups of inverse solution correspond to four different operating modes which cannot transit to each other smoothly. The workspace and the singularity trajectory of each mode are discussed. Based on the desired workspace, the geometry of the mechanism is determined. The operating mode of the mechanism is optimized according to distributing of all global and local performance indices on the workspace. The results are very useful for the design and application of the new manipulator with multiple forward and inverse solutions.

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.

The Dynamic Analysis of a 2-PRR Planar Parallel Mechanism

2005 ◽  
Vol 219 (9) ◽  
pp. 901-909 ◽  
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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