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.

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.

Failure recovery for wrench capability of wire-actuated parallel manipulators

Robotica ◽  
2011 ◽  
Vol 30 (6) ◽  
pp. 941-950 ◽  
Author(s):  
Leila Notash
Keyword(s):  
Failure Modes ◽  
Parallel Manipulators ◽  
Failure Recovery ◽  
Partial Recovery ◽  
Minimum Norm ◽  
Minimum Norm Solution ◽  
Actuator Failures ◽  
Force Moment ◽  
Hybrid Actuation

SUMMARYWire-actuated parallel manipulators and their failures are studied in this paper taking into consideration their failure modes. A methodology for investigating the effect of wire/actuator failures on the force/moment capability of manipulators is presented, and the criteria for full and partial recovery from these failures are established. The methodology is also applicable for the cases that the minimum norm solution for the vector of wire tensions gives a negative value for tension by treating the corresponding wire as failed. The proposed criteria are also valid for the manipulators that utilize hybrid actuation of wires and joints. Three planar wire-actuated parallel manipulators are used as the case study to illustrate the proposed methodology and criteria.

A geometric approach for singularity analysis of 3-DOF planar parallel manipulators using Grassmann–Cayley algebra

Robotica ◽  
2015 ◽  
Vol 35 (3) ◽  
pp. 511-520 ◽  
Author(s):  
Kefei Wen ◽  
TaeWon Seo ◽  
Jeh Won Lee
Keyword(s):  
Jacobian Matrix ◽  
Screw Theory ◽  
Geometric Approach ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Singular Configurations ◽  
Cayley Algebra ◽  
Grassmann Cayley Algebra ◽  
Planar Parallel Manipulators

SUMMARYSingular configurations of parallel manipulators (PMs) are special poses in which the manipulators cannot maintain their inherent infinite rigidity. These configurations are very important because they prevent the manipulator from being controlled properly, or the manipulator could be damaged. A geometric approach is introduced to identify singular conditions of planar parallel manipulators (PPMs) in this paper. The approach is based on screw theory, Grassmann–Cayley Algebra (GCA), and the static Jacobian matrix. The static Jacobian can be obtained more easily than the kinematic ones in PPMs. The Jacobian is expressed and analyzed by the join and meet operations of GCA. The singular configurations can be divided into three classes. This approach is applied to ten types of common PPMs consisting of three identical legs with one actuated joint and two passive joints.

Statics, Instantaneous Kinematics and Singularity Analysis of Planar Parallel Manipulators via Grassmann-Cayley Algebra

2014 ◽  
Vol 532 ◽  
pp. 378-381 ◽  
Author(s):  
Ke Fei Wen ◽  
Jeh Won Lee
Keyword(s):  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
New Approach ◽  
Coordinate Method ◽  
Cayley Algebra ◽  
Symbolic Formula ◽  
Grassmann Cayley Algebra ◽  
Planar Parallel Manipulators

The wrench Jacobian matrix plays an important role in statics and singularity analysis of planar parallel manipulators (PPMs). It is easy to obtain this matrix based on plücker coordinate method. In this paper, a new approach is proposed to the analysis of the forward and inverse wrench Jacobian matrix used by Grassmann-Cayley algebra (GCA). A symbolic formula for the inverse statics and a coordinate free formula for the singularity analysis are obtained based on this Jacobian. As an example, this approach is implemented for the 3-RPR PPMs.

Sensitivity Analysis of Planar Parallel Manipulators

2008 ◽  
Author(s):  
Ste´phane Caro ◽  
Nicolas Binaud ◽  
Philippe Wenger
Keyword(s):  
Sensitivity Analysis ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Geometric Parameters ◽  
Sensitivity Coefficients ◽  
Planar Parallel Manipulator ◽  
Moving Platform ◽  
Conditioning Number ◽  
Planar Parallel Manipulators

This paper deals with the sensitivity analysis of planar parallel manipulators. A methodology is introduced to derive the sensitivity coefficients by means of the study of 3-RPR manipulators. As a matter of fact, the sensitivity coefficients of the pose of its moving platform to variations in the geometric parameters are expressed algebraically, the variations being defined both in Polar and Cartesian coordinates. The dexterity of the manipulator is also studied by means of the conditioning number of its normalized kinematic Jacobian matrix. As an illustrative example, the sensitivity of a symmetrical planar parallel manipulator is analyzed in detail. Finally, the accuracy of the manipulator is compared with its dexterity.

Determination of singularity contours for five-bar planar parallel manipulators

Robotica ◽  
2000 ◽  
Vol 18 (5) ◽  
pp. 569-575 ◽  
Author(s):  
Gürsel Alıcı
Keyword(s):  
Parallel Manipulators ◽  
Joint Space ◽  
Point Of View ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Singular Configurations ◽  
Planning And Design ◽  
Prismatic Joints ◽  
Planar Parallel Manipulators

From a design point of view, it is crucial to predict singular configurations of a manipulator in terms of inputs in order to improve the dexterity and workspace of a manipulator. In this paper, we present a simple, yet a systematic appoach to obtain singularity contours for a class of five-bar planar parallel manipulators which are based on five rigid links and five single degree of freedom joints – revolute and prismatic joints. The determinants of the manipulator Jacobian matrices are evaluated in terms of joint inputs for a specified set of geometric parameters, and the contours of the determinants at 0.0 plane which are the singularity contours in joint space are generated for the three types of singularities reported in the literature. The proposed approach/algorithm is simple and systematic, and the resulting equations are easy to solve on a computer. The singularity contours for all the class are presented in order to demonstrate the method. It is concluded that the proposed method is useful in trajectory planning and design of five-bar planar parallel manipulators in order to improve their dexterity and workspace.

Adaptive and Singularity-Free Inverse Dynamics Models for Control of Parallel Manipulators With Actuation Redundancy

2011 ◽  
Author(s):  
Andreas Mu¨ller ◽  
Timo Hufnagel
Keyword(s):  
Range Of Motion ◽  
Inverse Dynamics ◽  
Null Space ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Torque Control ◽  
Alternative Formulation ◽  
Dynamics Model ◽  
Model Based ◽  
Control Forces

Redundant actuation of parallel kinematics machines (PKM) is a way to eliminate input-singularities and so to enlarge the usable workspace. From a kinematic point of view the number m of actuator coordinates exceeds the DOF δ of a redundantly actuated PKM (RA-PKM). The dynamics model, being the basis for model-based control, is usually expressed in terms of δ independent actuator coordinates. This implies that the model exhibits the same singularities as the non-redundant PKM, even though the RA-PKM is not singular. Consequently the admissible range of motion of the RA-PKM model is limited to that of the non-redundant PKM. In this paper an alternative formulation of the dynamics model in terms of the full set of m actuator coordinates is presented. It leads to a redundant system of m motion equations that is valid in the entire range of motion. This formulation gives rise to an inverse dynamics formulation tailored for real-time implementation. In contrast to the standard formulation in independent coordinates, the proposed inverse dynamics formulation does not involve control forces in the null space of the control matrix, i.e. it does not allow for the generation of internal prestresses, however. This is not problematic as the latter is usually not exploited. The proposed method is compared to the recently proposed adaptive coordinate switching method. Experimental results are reported if the inverse dynamics solution is introduced in model-based computed torque control scheme of a planar 2DOF RA-PKM.

Optimum design of 3-RRR planar parallel manipulators

2010 ◽  
Vol 224 (2) ◽  
pp. 411-418 ◽  
Author(s):  
Runliang Dou
Keyword(s):  
Optimum Design ◽  
Design Space ◽  
Jacobian Matrix ◽  
Kinematic Model ◽  
Parallel Manipulators ◽  
Stiffness Index ◽  
Geometrical Parameters ◽  
Dimensional Parameter ◽  
Planar Parallel Manipulators

This article deals with the optimum design of 3-RRR planar parallel manipulators. Based on the kinematic model and Jacobian matrix, the global conditioning index, global velocity index and global stiffness index of 3-RRR parallel manipulators are investigated. The corresponding atlases are represented graphically in the established design space, and the geometrical parameters without dimension are determined. An example is presented to achieve the optimum dimensional parameter based on the optimum non-dimensional result. The result of this article is not only useful for the development of 3-RRR planar parallel manipulators, but also helpful for the optimum design of other parallel manipulators.

Optimum synthesis of planar parallel manipulators based on kinematic isotropy and force balancing

Robotica ◽  
2004 ◽  
Vol 22 (1) ◽  
pp. 97-108 ◽  
Author(s):  
Gürsel Alıcı ◽  
Bijan Shirinzadeh
Keyword(s):  
Condition Number ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Kinematic Chains ◽  
Optimum Synthesis ◽  
Planar Parallel Manipulator ◽  
Distribution Parameters ◽  
Optimisation Procedure ◽  
Planar Parallel Manipulators

This paper deals with an optimum synthesis of planar parallel manipulators using two constrained optimisation procedures based on the minimization of: (i) the overall deviation of the condition number of manipulator Jacobian matrix from the ideal/isotropic condition number, and (ii) bearing forces throughout the manipulator workspace for force balancing. A revolute jointed planar parallel manipulator is used as an example to demonstrate the methodology. The parameters describing the manipulator geometry are obtained from the first optimisation procedure, and subsequently, the mass distribution parameters of the manipulator are determined from the second optimisation procedure based on force balancing. Optimisation results indicate that the proposed optimisation approach is systematic, versatile and easy to implement for the optimum synthesis of the parallel manipulator and other kinematic chains. This work contributes to previously published work from the point of view of being a systematic approach to the optimum synthesis of parallel manipulators, which is currently lacking in the literature.

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.

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