New dimensionally homogeneous jacobian matrix formulation by three end-effector points for optimal design of parallel manipulators

2003 ◽  
Vol 19 (4) ◽  
pp. 731-737 ◽  
Author(s):  
Sung-Gaun Kim ◽  
Jeha Ryu
Keyword(s):  
Optimal Design ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Matrix Formulation ◽  
End Effector ◽  
Dimensionally Homogeneous Jacobian Matrix

Dynamic Modeling of a Parallel Manipulator With Three Translational Degrees of Freedom

1998 ◽  
Author(s):  
Richard Stamper ◽  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Close Agreement ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Kinematic Structure ◽  
End Effector ◽  
Moving Platform ◽  
Euler Approach ◽  
Computationally Intensive

Abstract The dynamics of a parallel manipulator with three translational degrees of freedom are considered. Two models are developed to characterize the dynamics of the manipulator. The first is a traditional Lagrangian based model, and is presented to provide a basis of comparison for the second approach. The second model is based on a simplified Newton-Euler formulation. This method takes advantage of the kinematic structure of this type of parallel manipulator that allows the actuators to be mounted directly on the base. Accordingly, the dynamics of the manipulator is dominated by the mass of the moving platform, end-effector, and payload rather than the mass of the actuators. This paper suggests a new method to approach the dynamics of parallel manipulators that takes advantage of this characteristic. Using this method the forces that define the motion of moving platform are mapped to the actuators using the Jacobian matrix, allowing a simplified Newton-Euler approach to be applied. This second method offers the advantage of characterizing the dynamics of the manipulator nearly as well as the Lagrangian approach while being less computationally intensive. A numerical example is presented to illustrate the close agreement between the two models.

Determination of the Singularity Loci of Spherical Three-Degree-of-Freedom Parallel Manipularors

1992 ◽  
Author(s):  
Clément M. Gosselin ◽  
Jaouad Sefrioui
Keyword(s):  
Graphical Representation ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
End Effector ◽  
Cartesian Space ◽  
Singularity Locus ◽  
Three Degree Of Freedom ◽  
Analytical Expressions

Abstract In this paper, an algorithm for the determination of the singularity loci of spherical three-degree-of-freedom parallel manipulators with prismatic atuators is presented. These singularity loci, which are obtained as curves or surfaces in the Cartesian space, are of great interest in the context of kinematic design. Indeed, it has been shown elsewhere that parallel manipulators lead to a special type of singularity which is located inside the Cartesian workspace and for which the end-effector becomes uncontrollable. It is therfore important to be able to identify the configurations associated with theses singularities. The algorithm presented is based on analytical expressions of the determinant of a Jacobian matrix, a quantity that is known to vanish in the singular configurations. A general spherical three-degree-of-freedom parallel manipulator with prismatic actuators is first studied. Then, several particular designs are investigated. For each case, an analytical expression of the singularity locus is derived. A graphical representation in the Cartesian space is then obtained.

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.

Multi-Criteria Optimal Design of Parallel Manipulators Based on Natural Frequency

2010 ◽  
Vol 29-32 ◽  
pp. 2435-2442 ◽  
Author(s):  
Bang Jun Lv ◽  
S.J. Zhu ◽  
J.F. Xing
Keyword(s):  
Optimal Design ◽  
Natural Frequency ◽  
Parallel Manipulators ◽  
Average Frequency ◽  
Pareto Optimal Set ◽  
Large Size ◽  
Matrix Condition Number ◽  
Dimensionally Homogeneous Jacobian Matrix ◽  
Matrix Condition ◽  
Optimal Set

The Stewart manipulator has characteristics of low natural frequency, high cost and large size which make it difficult to obtain optimum performance with high dynamic response. The lowest natural frequency in the total workspace and average of six frequencies at home configuration of Stewart manipulator are introduced as indices to evaluate dynamic stability. Multi-criteria optimal design based on genetic algorithm (GA) was presented synthetically considering the workspace requirement, lowest natural frequency, average frequency and global dimensionally homogeneous Jacobian matrix condition number. An optimal result was obtained through standard GA using penalty function and the Pareto-optimal set was also obtained through parallel selection method.

Dynamics of a Class of Parallel Wrists

2003 ◽  
Vol 126 (3) ◽  
pp. 436-441 ◽  
Author(s):  
Raffaele Di Gregorio ◽  
Vincenzo Parenti-Castelli
Keyword(s):  
Jacobian Matrix ◽  
Dynamic Performance ◽  
Parallel Manipulators ◽  
Dynamic Problems ◽  
Performance Indices ◽  
Inverse Dynamic ◽  
End Effector ◽  
Kinematic Behavior ◽  
Effective Dynamic ◽  
Spherical Motion

This paper presents a dynamic model of parallel wrists with all links constrained to have a spherical motion with the same center. The model can also be applied to serial wrists. The model, based on Lagrangian formulation of dynamics, exploits the feature that all the links have the same fixed point. Three parameters defining the platform orientation are used as generalized coordinates. This choice allows the use of the generalized inertia matrix (GIM) appearing in the model to calculate effective dynamic performance indices proposed in a previous paper. The model can solve both the direct and the inverse dynamic problems. It also contains the Jacobian matrix useful to characterize the kinematic behavior of parallel manipulators. By the model it is shown that the best performances are reached in the workspace regions where the manipulator has a good kinematic and dynamic isotropy, whereas the incidence of nonlinear forces on performances is relevant at high end-effector speed. A numerical example is provided.

Real-Time Forward Position Kinematics of the Spatial Parallel Manipulator

2013 ◽  
Vol 712-715 ◽  
pp. 2241-2248
Author(s):  
Jian Wei Mi ◽  
Li Du ◽  
Xue Chao Duan
Keyword(s):  
Real Time ◽  
High Precision ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Time Algorithm ◽  
Initial Position ◽  
End Effector ◽  
Time Consumption ◽  
Online Implementation

Aiming at online implementation, a real-time algorithm for forward position kinematics of the parallel manipulators is proposed, in which the steepest decent direction of the solution iteration is constructed with Jacobian matrix, with the initial position for iteration arbitrarily chosen from the workspace. Under the condition of motion continuity of the end-effector, the unique forward position kinematics solution can be found out with this algorithm. Forward position kinematics case studies of spatial parallel manipulators were conducted, which show that the algorithm has the advantages of a high precision, little iteration and less millisecond-level time consumption.

Angularity and axiality of a Schönflies parallel manipulator

Robotica ◽  
2015 ◽  
Vol 34 (11) ◽  
pp. 2415-2439 ◽  
Author(s):  
J. Jesús Cervantes-Sánchez ◽  
José M. Rico-Martínez ◽  
Víctor H. Pérez-Muñoz
Keyword(s):  
Velocity Field ◽  
Parallel Manipulator ◽  
Velocity Vector ◽  
Systematic Approach ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Mobile Platform ◽  
Angular Velocity Vector ◽  
Numerical Examples ◽  
Dimensionally Homogeneous Jacobian Matrix

SUMMARYThis paper presents a systematic approach to compute the angularity and the axiality indices for a Schönflies parallel manipulator. Angularity index may be considered as a measure of the sensitivity of the mobile platform to changes in rotation, while axiality index can be used to measure the sensitivity of the OP of the mobile platform to changes 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 meaning, which may be useful to the designer of parallel manipulators. Moreover, both dexterity 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. Detailed numerical examples are given in order to illustrate the computation of the dexterity indices.

On the Solutions of Interval Systems for Under-Constrained and Redundant Parallel Manipulators

2017 ◽  
Vol 9 (6) ◽  
Author(s):  
Leila Notash
Keyword(s):  
Least Squares ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Constrained Systems ◽  
Solution Set ◽  
Least Squares Solution ◽  
Interval Linear ◽  
Interval Linear Systems ◽  
Parameter Dependency ◽  
Interval Systems

For under-constrained and redundant parallel manipulators, the actuator inputs are studied with bounded variations in parameters and data. Problem is formulated within the context of force analysis. Discrete and analytical methods for interval linear systems are presented, categorized, and implemented to identify the solution set, as well as the minimum 2-norm least-squares solution set. The notions of parameter dependency and solution subsets are considered. The hyperplanes that bound the solution in each orthant characterize the solution set of manipulators. While the parameterized form of the interval entries of the Jacobian matrix and wrench produce the minimum 2-norm least-squares solution for the under-constrained and over-constrained systems of real matrices and vectors within the interval Jacobian matrix and wrench vector, respectively. Example manipulators are used to present the application of methods for identifying the solution and minimum norm solution sets for actuator forces/torques.

scholarly journals Kinematic Synthesis of Tendon-Driven Manipulators with Isotropic Transmission Characteristics

1993 ◽  
Vol 115 (4) ◽  
pp. 884-891 ◽  
Author(s):  
Yeong-Jeong Ou ◽  
Lung-Wen Tsai
Keyword(s):  
Jacobian Matrix ◽  
Null Vector ◽  
Force Distribution ◽  
Force Transmission ◽  
Transmission Characteristics ◽  
Kinematic Synthesis ◽  
End Effector ◽  
Structure Matrix ◽  
Applied Forces ◽  
Matrix Design

This paper presents a methodology for kinematic synthesis of tendon-driven manipulators with isotropic transmission characteristics. The force transmission characteristics, from the end-effector space to the actuator space, has been investigated. It is shown that tendon forces required to act against externally applied forces are functions of the structure matrix, its null vector, and the manipulator Jacobian matrix. Design equations for synthesizing a manipulator to possess isotropic transmission characteristics are derived. It is shown that manipulators which possess isotropic transmission characteristics have much better force distribution among their tendons.

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