WORKSPACE OF WIRE-ACTUATED PARALLEL MANIPULATORS AND VARIATIONS IN DESIGN PARAMETERS

2013 ◽  
Vol 37 (2) ◽  
pp. 215-229 ◽  
Author(s):  
Vahid Nazari ◽  
Leila Notash
Keyword(s):  
Jacobian Matrix ◽  
Null Space ◽  
Parallel Manipulators ◽  
Mobile Platform ◽  
Design Parameters ◽  
Balance Equations ◽  
Size And Shape ◽  
Workspace Analysis ◽  
Force Moment ◽  
Simulation Results

The purpose of the paper is to investigate the effect of small variations (uncertainties) and large variations in design parameters on the size and shape of the workspace of the wire-actuated parallel manipulators. The static force/moment balance equations, taking into account the null space of the Jacobian matrix, are used for the workspace analysis. The parameters examined include: the winding direction of wires on the pulleys; the radius of the pulley; the orientation, radius, and mass of the mobile platform; the peg length; and the ratio of the peg radii at the entrance and exit. Also, the effect of the geometric arrangement of wire attachment points and the number of wire connection points on the mobile platform, on the size and shape of the workspace is considered. The simulation results show the effect of small and large variations in the aforementioned parameters on the workspace of wire-actuated parallel manipulators without and with gravity.

Analysis of Active Joint Failure in Parallel Robot Manipulators

2004 ◽  
Vol 126 (6) ◽  
pp. 959-968 ◽  
Author(s):  
Mahir Hassan ◽  
Leila Notash
Keyword(s):  
Jacobian Matrix ◽  
Null Space ◽  
Robot Manipulators ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Task Space ◽  
Active Joint ◽  
Joint Failure ◽  
Space Vectors ◽  
Six Degree Of Freedom

In this study, the effect of active joint failure on the mobility, velocity, and static force of parallel robot manipulators is investigated. Two catastrophic active joint failure types are considered: joint jam and actuator force loss. To investigate the effect of failure on mobility, the Gru¨bler’s mobility equation is modified to take into account the kinematic constraints imposed by various branches in the manipulator. In the case of joint jam, the manipulator loses the ability to move and apply force in a specific portion of its task space; while in the case of actuator force loss, the manipulator gains an unconstrained motion in a specific portion of the task space in which an externally applied force cannot be resisted by the actuator forces. The effect of joint jam and actuator force loss on the velocity and on the force capabilities of parallel manipulators is investigated by examining the change in the Jacobian matrix, its inverse, and transposes. It is shown that the reduced velocity and force capabilities after joint jam and loss of actuator force could be determined using the null space vectors of the transpose of the Jacobian matrix and its inverse. Computer simulation is conducted to demonstrate the application of the developed methodology in determining the post-failure trajectory of a 3-3 six-degree-of-freedom Stewart-Gough manipulator, when encountering active joint jam and actuator force loss.

Two Natural Dexterity Indices for Parallel Manipulators: Angularity and Axiality

2014 ◽  
Vol 6 (4) ◽  
Author(s):  
J. Jesús Cervantes-Sánchez ◽  
J. M. Rico-Martínez ◽  
V. H. Pérez-Muñoz
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Mobile Platform ◽  
Angular Velocity Vector ◽  
Motion Sensitivity ◽  
Physical Insight ◽  
Dimensionally Homogeneous Jacobian Matrix ◽  
The One ◽  
General Motion

This paper introduces two novel dexterity indices, namely, angularity and axiality, which are used to estimate the motion sensitivity of the mobile platform of a parallel manipulator undergoing a general motion involving translation and rotation. On the one hand, the angularity index can be used to measure the sensitivity of the mobile platform to change in rotation. On the other hand, the axiality index can be used to measure the sensitivity of the operation point (OP) of the mobile platform to change in translation. Since both indices were inspired by very fundamental concepts of classical kinematics (angular velocity vector and helicoidal velocity field), they offer a clear and simple physical insight, which is expected to be meaningful to the designer of parallel manipulators. Moreover, the proposed indices do not require obtaining a dimensionally homogeneous Jacobian matrix, nor do they depend on having similar types of actuators in each manipulator's leg. The details of the methodology are illustrated by considering a classical parallel manipulator.

Orientation Workspace Analysis of 6-DOF Parallel Manipulators

1999 ◽  
Author(s):  
Ilian A. Bonev ◽  
Jeha Ryu
Keyword(s):  
Fixed Point ◽  
Direct Method ◽  
Parallel Manipulators ◽  
Mobile Platform ◽  
Euler Angles ◽  
Discretization Method ◽  
Workspace Analysis ◽  
A Direct Method ◽  
Orientation Workspace

Abstract This paper presents a new discretization method for the computation of the orientation workspace of 6-rDOF parallel manipulators, defined as the set of all attainable orientations of the mobile platform about a fixed point. The method is based on the use of a modified set of Euler angles and a particular representation of the orientation workspace. In addition, a direct method is suggested for the computation of the projected orientation workspace, defined as the set of all possible directions of the approach vector of the mobile platform. Alternative ways of computing these two types of workspaces are also discussed with typical examples.

FORCE-MOMENT CAPABILITIES OF REVOLUTE-JOINTED PLANAR PARALLEL MANIPULATORS WITH ADDITIONAL ACTUATED BRANCHES

2007 ◽  
Vol 31 (4) ◽  
pp. 469-481 ◽  
Author(s):  
Flavio Firmani ◽  
Alp Zibil ◽  
Scott B. Nokleby ◽  
Ron P. Podhorodeski
Keyword(s):  
Parallel Manipulators ◽  
Mobile Platform ◽  
Maximum Force ◽  
Maximum Moment ◽  
Force Moment ◽  
Redundantly Actuated ◽  
Planar Parallel Manipulators

The force-moment capabilities of revolute-jointed planar parallel manipulators (PPMs) are presented. A previously developed analysis that determines explicitly the force-moment capabilities of parallel manipulators is considered and the formulation is improved. This analysis is based upon properly adjusting the actuator outputs to their maximum capabilities. The force-moment capabilities of two actuation layouts are investigated: the non-redundant 3-RRR PPM and the redundantly actuated 4-RRR PPM, where the underline indicates the actuated joint. Four studies of force-moment capabilities are presented: maximum force with a prescribed moment, maximum applicable force, maximum moment with a prescribed force, and maximum applicable moment. These studies are performed for constant payload orientation of the mobile platform throughout the manipulator’s workspace. It is concluded that the manipulator with the additional actuated branch shows an improvement of the force-moment capabilities at the expense of reducing its workspace.

Wrench capabilities of planar parallel manipulators. Part II: Redundancy and wrench workspace analysis

Robotica ◽  
2008 ◽  
Vol 26 (6) ◽  
pp. 803-815 ◽  
Author(s):  
Flavio Firmani ◽  
Alp Zibil ◽  
Scott B. Nokleby ◽  
Ron P. Podhorodeski
Keyword(s):  
Parallel Manipulators ◽  
Mobile Platform ◽  
Operational Cost ◽  
Performance Indices ◽  
Workspace Analysis ◽  
Redundantly Actuated ◽  
Comparison Of The Results ◽  
Actuated Joints ◽  
Planar Parallel Manipulators

SUMMARYThis part of the paper investigates the wrench capabilities of redundantly actuated planar parallel manipulators (PPMs). The wrench capabilities of PPMs are determined by mapping a hypercube from the torque space into a polytope in the wrench space. For redundant PPMs, one actuator output capability constrains the wrench space with a smaller polytope that is contained inside the overall polytope. Performance indices are derived from six study cases. These indices are employed to analyze the wrench workspace for constant orientation of the mobile platform of the non-redundant 3-RRR PPM, and actuation redundant 4-RRR and 3-RRR PPMs, where the underline indicates the actuated joints. A comparison of the results shows that both of the redundantly-actuated PPMs give better wrench capabilities than the non-redundant PPM. However, it is shown that scaled for the operational cost (wrench capabilities divided by total actuation output) the non-redundant 3-RRR PPM provides the highest maximum reachable force, the 3-RRR PPM produces the highest isotropic force, and the 4-RRR yields the highest reachable moment.

Workspace Investigation of Wire-Actuated Parallel Manipulators With Uncertainties in Wire Connections

2010 ◽  
Author(s):  
Leila Notash ◽  
Derek McColl
Keyword(s):  
Parallel Manipulators ◽  
Mobile Platform ◽  
Static Force ◽  
Force Moment ◽  
Geometric Representations ◽  
The Wire

In this article, the effect of uncertainties in wire connections on the workspace generation of wire-actuated parallel manipulators is investigated. The geometric representations of uncertainties in the attachments points of wires to the base and to the mobile platform are developed. Two methods for workspace generation with uncertainty are presented. The first method is based on the calculation of positive wire tensions derived from the static force/moment balance. The second method is based on the direction of the wire forces applied to the mobile platform, and does not take into account the wire tensions. The proposed methods are applied for the workspace generation of two planar wire-actuated parallel manipulators.

MOTION RECOVERY AFTER JOINT FAILURE IN PARALLEL MANIPULATORS

2011 ◽  
Vol 35 (4) ◽  
pp. 559-571 ◽  
Author(s):  
Leila Notash
Keyword(s):  
Failure Modes ◽  
Jacobian Matrix ◽  
Null Space ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Partial Recovery ◽  
Joint Failure ◽  
Motion Recovery ◽  
Motion Performance ◽  
Planar Parallel Manipulators

In this paper, the failure of parallel manipulators is investigated. Failure modes of parallel manipulators and their causes and effects from the kinematics point of view are discussed. Methodologies for investigating the effect of failures, due to joint failure or singularity, on the motion performance of manipulators are presented, and the criteria for full and partial recovery from these failures are established. The proposed methodologies are based on the projection of the lost motion onto the orthogonal complement of the null space of the Jacobian matrix after failure. The procedure is simulated for planar parallel manipulators to examine if after joint failure the required motion of manipulator could be fully recovered; as well as to calculate the corrections to the motion of remaining joints for recovering the lost motion.

Solving Jacobian Matrix of Parallel Manipulators With Linear Driving Limbs by Using CAD Variation Geometric Approach

2006 ◽  
Author(s):  
Yi Lu ◽  
Bo Hu
Keyword(s):  
Computer Simulation ◽  
Jacobian Matrix ◽  
Geometric Approach ◽  
Parallel Manipulators ◽  
Partial Derivatives ◽  
Important Index ◽  
Simulation Results ◽  
Dynamics Analyses

The velocity Jacobian matrix and the force Jacobian matrix are important index for kinematics, singularity and dynamics analyses of parallel manipulators. A novel computer variation geometric approach is proposed for solving the velocity Jacobian matrix and the force Jacobian matrix of parallel manipulators with linear driving limbs, as well as the determinant of Jacobian matrix. First, basic computer variation geometry techniques and definitions are presented for designing the simulation mechanisms, and several simulation mechanisms of parallel manipulators with linear driving limbs are created. Second, some velocity simulation mechanisms are created and the partial derivatives in Jacobian matrix are solved automatically and visualized dynamically. Based on the results of the computer simulation, the velocity Jacobian matrix and force Jacobian matrix are formed and the determinant of Jacobian matrix is solved. Moreover, the simulation results prove that the computer variation geometry approach is fairly quick and straightforward, and is accurate and repeatable. This project is supported by NSFC No. 50575198.

scholarly journals Workspace Analysis of 6-PRRS Parallel Manipulators Based on the Vertex Space Concept

1999 ◽  
Author(s):  
Ilian A. Bonev ◽  
Jeha Ryu
Keyword(s):  
Parallel Manipulators ◽  
The Other ◽  
Design Parameters ◽  
Geometric Algorithm ◽  
Workspace Analysis ◽  
Cad Cam ◽  
Space Concept ◽  
Orientation Workspace

Abstract This paper presents workspace analysis of 6–PRRS parallel manipulators based on the vertex space concept. A fully geometric algorithm is described for the computation of the constant-orientation workspace, which was implemented in the CAD/CAM system CATIA. The influence of the different design parameters on the workspace as well as on the other properties of the manipulator is discussed. Finally, examples are provided to demonstrate the usefulness of the proposed method.

Analysis of a High Stiffness Warehousing Cable-Based Robot

2014 ◽  
Author(s):  
Sergio Torres-Mendez ◽  
Amir Khajepour
Keyword(s):  
Static Analysis ◽  
Mechanical Analysis ◽  
Mobile Platform ◽  
Forward Kinematics ◽  
High Stiffness ◽  
Workspace Analysis ◽  
Simulation Results ◽  
Planar Motions

This paper presents and analyzes a novel architecture for a fully constrained cable-based robot that is used in warehousing tasks. A mobile platform is connected to a static box by a set of twelve cables; the cables arrangement allows the mobile platform to achieve stiff positions with constant orientation along with large planar motions. The mechanical analysis of the robot includes inverse and forward kinematics, as well as static analysis and stiffness models. In addition, a workspace analysis describes the feasible boundaries for the suspended and fully constrained cases. Then, the stiffness attributes for both cases are analyzed and discussed. Simulation results show that the proposed robot meets the warehousing requirements of large workspace, high stiffness, and low force input.

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