The Optimum Quality Index for a Spatial Redundant 8-8 In-Parallel Manipulator

2000 ◽  
Author(s):  
Yu Zhang ◽  
Joseph Duffy ◽  
Carl D. Crane
Keyword(s):  
Quality Index ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Static Stability ◽  
Space Structure ◽  
Maximum Value ◽  
Deployable Space Structure ◽  
Symmetrical Configuration ◽  
Dimensionless Ratio ◽  
Optimal Quality

Abstract The quality index for a redundant 4-4 in-parallel manipulator with a square platform and a square base was obtained in [1]. Following this, the quality index for a redundant 4-8 manipulator with a square platform and an octagonal base was determined in [2]. In this paper the optimal quality index for a redundant 8-8 manipulator is determined. The device has an octagonal platform and a similar octagonal base connected by eight legs. The quality index is defined as a dimensionless ratio which takes a maximum value of 1 at a central symmetrical configuration that is shown to correspond to the maximum value of the square root of the determinant of the product of the manipulator Jacobian by its transpose. The Jacobian matrix is none other than the normalized coordinates of the eight leg lines. It is shown that the quality index can be used as a constructive measure of not only acceptable and optimum design proportions but also an acceptable operating workspace (in the static stability sense). The analysis of the redundant 8-8 manipulator described here can be used to model and design a self-deployable space structure that has a pair of flexible octagonal antenna platforms in the base and top platform.

The Optimum Quality Index for the Stability of In-Parallel Planar Platform Devices

1999 ◽  
Vol 121 (1) ◽  
pp. 15-20 ◽  
Author(s):  
J. Lee ◽  
J. Duffy ◽  
M. Keler
Keyword(s):  
Optimal Design ◽  
Equilateral Triangle ◽  
Quality Index ◽  
Optimal Shape ◽  
Geometrical Meaning ◽  
Moving Platforms ◽  
Maximum Value ◽  
Dimensionless Ratio ◽  
Parallel Platform ◽  
The Stability

The paper investigates primarily the geometrical meaning of the determinant of the Jacobian (det j) of the three connector lines of a planar in-parallel platform device using reciprocity. A remarkably simple result is deduced: The maximum value of det j namely, det jm is simply one-half of the sum of the lengths of the sides of the moving triangular platform. Further, this result is shown to be independent of the location of the fixed pivots in the base. A dimensionless ratio λ = |det j|/det jm is defined as the quality index (0 ≤ λ ≤ 1) and it is proposed here to use it to measure “closeness” to a singularity. An example which determines the optimal design by comparing different shaped moving platforms having the same det jm is given and demonstrates that the optimal shape is in fact an equilateral triangle

The Optimum Quality Index for the Stability of In-Parallel Planar Platform Devices

1996 ◽  
Author(s):  
Jaehoon Lee ◽  
Joseph Duffy ◽  
Max Keler
Keyword(s):  
Optimal Design ◽  
Equilateral Triangle ◽  
Quality Index ◽  
Optimal Shape ◽  
Geometrical Meaning ◽  
Moving Platforms ◽  
Maximum Value ◽  
Dimensionless Ratio ◽  
Parallel Platform ◽  
The Stability

Abstract The paper investigates primarily the geometrical meaning of the determinant of the Jacobian (det j) of the three connector lines of a planar in-parallel platform device using reciprocity. A remarkably simple result is deduced : The maximum value of det j namely, det jm is simply one-half of the sum of the lengths of the sides of the moving triangular platform. Further, this result is shown to be independent of the location of the fixed pivots in the base. A dimensionless ratio λ = |det j| / det jm is defined as the quality index (0 ≤ λ ≤ 1) and it is proposed here to use it to measure “closeness” to a singularity. An example which determines the optimal design by comparing different shaped moving platforms having the same det jm is given and demonstrates that the optimal shape is in fact an equilateral triangle.

Ultralight Deployable Space Structure Prototype

2020 ◽  
Author(s):  
Eleftherios Gdoutos ◽  
Alan Truong ◽  
Antonio Pedivellano ◽  
Fabien Royer ◽  
Sergio Pellegrino
Keyword(s):  
Space Structure ◽  
Deployable Space Structure

Design and analysis of CICABOT: a novel translational parallel manipulator based on two 5-bar mechanisms

Robotica ◽  
2011 ◽  
Vol 30 (3) ◽  
pp. 449-456 ◽  
Author(s):  
M. F. Ruiz-Torres ◽  
E. Castillo-Castaneda ◽  
J. A. Briones-Leon
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Geometric Analysis ◽  
Vector Equation ◽  
Prismatic Joints ◽  
Hollow Cylinders ◽  
Moving Platform ◽  
Direct Kinematics

SUMMARYThis work presents the CICABOT, a novel 3-DOF translational parallel manipulator (TPM) with large workspace. The manipulator consists of two 5-bar mechanisms connected by two prismatic joints; the moving platform is on the union of these prismatic joints; each 5-bar mechanism has two legs. The mobility of the proposed mechanism, based on Gogu approach, is also presented. The inverse and direct kinematics are solved from geometric analysis. The manipulator's Jacobian is developed from the vector equation of the robot legs; the singularities can be easily derived from Jacobian matrix. The manipulator workspace is determined from analysis of a 5-bar mechanism; the resulting workspace is the intersection of two hollow cylinders that is much larger than other TPM with similar dimensions.

Jacobian Analysis of a Fully Decoupled Parallel Manipulator for Minimally Invasive Surgery

2012 ◽  
Author(s):  
Chin-Hsing Kuo ◽  
Jian S. Dai
Keyword(s):  
Minimally Invasive Surgery ◽  
Minimally Invasive ◽  
Invasive Surgery ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Central Point ◽  
Special Structure ◽  
Jacobian Matrices ◽  
Singular Configurations ◽  
Reachable Workspace

This paper presents the Jacobian analysis of a parallel manipulator that has a fully decoupled 4-DOF remote center-of-motion for application in minimally invasive surgery. Owing to the special structure of the manipulator, the Jacobian matrix of the manipulator is expressed as a combination of three special Jacobian matrices, namely the Jacobian of motion space, Jacobian of constraints, and Jacobian of actuations. Based on these Jacobian matrices, the singular configurations of the manipulator are then identified. It shows that the configuration singularity only exists at the central point and the boundary of the reachable workspace of the manipulator.

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.

scholarly journals Design and Analysis of a Wire-Driven Parallel Mechanism for Low-Gravity Environment Simulation

2014 ◽  
Vol 6 ◽  
pp. 810606 ◽  
Author(s):  
Weifang Wang ◽  
Xiaoqiang Tang ◽  
Zhufeng Shao ◽  
Jiping Yang ◽  
Wangmin Yi
Keyword(s):  
Parallel Mechanism ◽  
Quality Index ◽  
Parallel Manipulator ◽  
Force Distribution ◽  
The Moon ◽  
Low Gravity ◽  
Wire Tension ◽  
Environment Simulation ◽  
The Wire ◽  
And Control

Traditional simulation mechanisms are unable to meet the simulation requirements of spacecraft launcher in low-gravity environment, like in the Moon. Based on the advantages of wire-driven parallel mechanism, a 6-DOF low-gravity environment simulation device with eight wires is designed in this paper. Firstly, the configuration and dimensional design of this wire-driven parallel mechanism are carried out. To operate and control the wire-driven parallel mechanism, a force distribution algorithm is introduced and the workspace is analyzed. Then, an evaluation index named quality index is established in order to study the performance of the wire-driven parallel manipulator in its workspace and reasonable tension is obtained after analyzing the influence on quality index caused by different wire tension.

Design and analysis of a totally decoupled 3-DOF spherical parallel manipulator

Robotica ◽  
2010 ◽  
Vol 29 (7) ◽  
pp. 1093-1100 ◽  
Author(s):  
Dan Zhang ◽  
Fan Zhang
Keyword(s):  
Physical Meaning ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Degree Of Freedom ◽  
Redundant Constraints ◽  
Rotational Motions ◽  
Spherical Parallel Manipulator

SUMMARYIn this paper, we propose a unique, decoupled 3 degree-of-freedom (DOF) parallel wrist. The condition required for synthesizing a fully isotropic parallel mechanism is obtained on the basis of the physical meaning of the row vector in the Jacobian matrix. Specifically, an over-constrained spherical 3-DOF parallel mechanism is presented and the modified structure, which avoids the redundant constraints, is also introduced. The proposed manipulator is capable of decoupled rotational motions around the x, y, and z axes and contains an output angle that is equal to the input angle. As this device is analyzed with the Jacobian matrix, the mechanism is free of singularity within its workspace and maintains homogenous stiffness over the entire workspace.

Sign in / Sign up

Export Citation Format

Share Document