A Simple Method for Mobility Analysis Using Reciprocal Screws

2006 ◽  
Author(s):  
Z. Huang ◽  
Q. J. Ge
Keyword(s):  
Coordinate System ◽  
Scalar Product ◽  
Simple Procedure ◽  
Parallel Manipulators ◽  
Simple Expression ◽  
Parallel Mechanisms ◽  
Complex Mechanism ◽  
Mobility Analysis ◽  
Simple Method ◽  
Analysis Process

The goal of this paper is to demonstrate that the Modified Gru¨bler-Kutzbach Criterion when combined with a simple procedure for determining the reciprocal screws offers a direct and simple method for analysing highly complex mechanisms including the over-constrained parallel manipulators. Since the scalar product of screws is not dependent on the choice of the origin, one can quickly obtain a simple expression of screws by selecting an appropriate coordinate system. In such simple expression, the coordinates of a screw would include 0 or 1, and thus greatly simplifies the procedure for determine the number of constraints in a mechanism. Seven rules have been presented to help simplify the analysis process. The advocated approach makes it possible to determine, within minutes, the mobility of a highly complex mechanism by using a pencil and a paper. Many over-constrained mechanisms, including three parallel mechanisms, are presented as examples.

Forward and Inverse Acceleration Analyses of In-Parallel Manipulators

1998 ◽  
Vol 122 (3) ◽  
pp. 299-303 ◽  
Author(s):  
Jose´ Marı´a Rico Martı´nez ◽  
Joseph Duffy
Keyword(s):  
Parallel Manipulator ◽  
Computing Time ◽  
Parallel Manipulators ◽  
Simple Expression ◽  
Intermediate Step ◽  
Simple Method ◽  
Dynamics And Control ◽  
Klein Form ◽  
Six Degree Of Freedom ◽  
And Control

Simple expressions for the forward and inverse acceleration analyses of a six degree of freedom in-parallel manipulator are derived. The expressions are obtained by firstly computing the “accelerator” for a single Hooke-Prismatic-Spheric, HPS for short, connector chain in terms of the joint velocities and accelerations. The accelerator is a function of the line coordinates of the joint axes and of a sequence of Lie products of the same line coordinates. A simple expression for the acceleration of the prismatic actuator is obtained by forming the Klein form, or reciprocal product, with the accelerator and the coordinates of the line of the connector chain. Since the Klein form is invariant, the resulting expression can be applied directly to the six HPS connector chains of an in-parallel manipulator. As a required intermediate step, this contribution also derives the corresponding solutions for the forward and inverse velocity analyses. The authors believe that this simple method has applications in the dynamics and control of these in-parallel manipulators where the computing time must be minimized to improve the behavior of parallel manipulators. [S1050-0472(00)01303-9]

An Efficient Inverse Acceleration Analysis of In-Parallel Manipulators

1996 ◽  
Author(s):  
José María Rico Martínez ◽  
Joseph Duffy
Keyword(s):  
Parallel Manipulator ◽  
Computing Time ◽  
Parallel Manipulators ◽  
Simple Expression ◽  
Degree Of Freedom ◽  
Simple Method ◽  
Dynamics And Control ◽  
Acceleration Analysis ◽  
Klein Form ◽  
And Control

Abstract A very simple novel expression for the accelerations of the six prismatic actuators, of the HPS connector chains, of a 6 degree of freedom in-parallel manipulator is derived. The expression is obtained by firstly computing the “accelerator” for a single HPS connector chain in terms of the joint velocities and accelerations. The accelerator is a function of the line coordinates of the joint axes and of a sequence of Lie products of the same line coordinates. A simple expression for the acceleration of the prismatic actuator is obtained by forming the Klein form, or reciprocal product, with the accelerator and the coordinates of the line of the connector chain. Since the Klein form is invariant, the resulting expression can be applied directly to the six HPS connector chains of an in-parallel manipulator. The authors believe that this simple method has important applications in the dynamics and control of these in-parallel manipulators where the computing time must be minimized to improve the behavior of parallel manipulators.

Modeling and Analysis of Parallel Mechanisms With Both Kinematic and Actuation Redundancies Via Screw Theory

2017 ◽  
Vol 9 (6) ◽  
Author(s):  
Long Kang ◽  
Wheekuk Kim ◽  
Byung-Ju Yi
Keyword(s):  
Screw Theory ◽  
Parallel Manipulators ◽  
Static Force ◽  
Parallel Mechanisms ◽  
Kinematic Redundancy ◽  
Mobility Analysis ◽  
Modeling And Analysis ◽  
Actuation Redundancy ◽  
Force Relationship

Two kinds of mechanical redundancies, namely kinematic redundancy and actuation redundancy, have been extensively studied due to their advantageous features in autonomous industry. Screw theory has been successfully applied to develop an analytical Jacobian of nonredundant parallel manipulators (PMs). However, to the best of our knowledge, screw theory has not been attempted for modeling of PMs with kinematic redundancies. Thus, first, through the mobility analysis of a simple nonredundant planar PM and its variations, this paper reviews kinematic and actuation redundancy systematically. Then, we demonstrated how to derive analytical Jacobian and also static force relationship for a PM with both kinematic and actuation redundancies by using the screw theory. Finally, simulations were performed to demonstrate the advantageous features of kinematic and actuation redundancies.

scholarly journals Introduction to the special issue: parallel manipulators.

Robotica ◽  
1997 ◽  
Vol 15 (4) ◽  
pp. 353-353
Author(s):  
François Pierrot
Keyword(s):  
North America ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
Parallel Mechanisms ◽  
Special Issue ◽  
Industrial Areas

It has been a pleasure for me to arrange this Special Issue of Robotica on Parallel Robots which provides 9 papers from authors from Asia, Oceania, North America and Europe; worldwide research on this topic is proof of the growing interest of both the scientific and the industrial areas of parallel mechanisms. I truly believe that the main reason for this enthusiasm is that parallel mechanisms research extends from theoretical mathematics and kinematics to applied robotics, and even beyond, creating new technological challenges.

scholarly journals Heterogeneous Catalytic Synthesis of 2-Methylbenzimidazole from 2-Nitroaniline and Ethanol Over Mg Modified Cu-Pd/γ-Al2O3

Catalysts ◽  
2018 ◽  
Vol 9 (1) ◽  
pp. 8 ◽  
Author(s):  
Feng Feng ◽  
Yaqin Deng ◽  
Zheng Cheng ◽  
Xiaoliang Xu ◽  
Qunfeng Zhang ◽  
...  
Keyword(s):  
Active Sites ◽  
Hydrogen Transfer ◽  
High Efficiency ◽  
Simple Procedure ◽  
Direct Synthesis ◽  
Reaction System ◽  
Simple Method ◽  
Heterogeneous Catalytic ◽  
Coupled Reaction ◽  
Al2o3 Catalyst

The direct synthesis of benzimidazoles from 2-nitroaniline and ethanol over Cu-Pd/γ-Al2O3 catalysts has the advantages of requiring easily available starting materials, having high efficiency, and a simple procedure. The modification by Mg of the Cu-Pd/γ-Al2O3 catalyst could improve the catalytic activity significantly. The addition of Mg to the Cu-Pd/γ-Al2O3 catalyst could maintain and promote the formation of CuPd alloy active sites. Meanwhile, the basicity of the support was enhanced appropriately by Mg, which generated more basic sites (Al-Oδ−) to accelerate the dehydrogenation of alcohol and increased the rate of the whole coupled reaction. The 2-nitroaniline was completely converted over Cu-Pd/(Mg)γ-Al2O3 after reacting for six hours, and the yield of 2-methylbenzimidazole was 98.8%. The results of this work provide a simple method to develop a more efficient catalyst for the “alcohol-dehydrogenation, hydrogen transfer and hydrogenation” coupled reaction system.

A Statically Balanced Gough/Stewart-Type Platform: Conception, Design, and Simulation

2009 ◽  
Vol 1 (3) ◽  
Author(s):  
Marco Carricato ◽  
Clément Gosselin
Keyword(s):  
Sufficient Conditions ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Theoretical Point ◽  
Constant Force ◽  
Parallel Mechanisms ◽  
End Effector ◽  
Neutral Equilibrium ◽  
The Difference ◽  
Elastic Elements

Gravity compensation of spatial parallel manipulators is a relatively recent topic of investigation. Perfect balancing has been accomplished, so far, only for parallel mechanisms in which the weight of the moving platform is sustained by legs comprising purely rotational joints. Indeed, balancing of parallel mechanisms with translational actuators, which are among the most common ones, has been traditionally thought possible only by resorting to additional legs containing no prismatic joints between the base and the end-effector. This paper presents the conceptual and mechanical designs of a balanced Gough/Stewart-type manipulator, in which the weight of the platform is entirely sustained by the legs comprising the extensible jacks. By the integrated action of both elastic elements and counterweights, each leg is statically balanced and it generates, at its tip, a constant force contributing to maintaining the end-effector in equilibrium in any admissible configuration. If no elastic elements are used, the resulting manipulator is balanced with respect to the shaking force too. The performance of a study prototype is simulated via a model in both static and dynamic conditions, in order to prove the feasibility of the proposed design. The effects of imperfect balancing, due to the difference between the payload inertial characteristics and the theoretical/nominal ones, are investigated. Under a theoretical point of view, formal and novel derivations are provided of the necessary and sufficient conditions allowing (i) a body arbitrarily rotating in space to rest in neutral equilibrium under the action of general constant-force generators, (ii) a body pivoting about a universal joint and acted upon by a number of zero-free-length springs to exhibit constant potential energy, and (iii) a leg of a Gough/Stewart-type manipulator to operate as a constant-force generator.

A Simple Method for Inverse Kinematic Analysis of the General 6R Serial Robot

2006 ◽  
Author(s):  
Zhi Xin Shi ◽  
Yu Feng Luo ◽  
Lu Bing Hang ◽  
Ting Li Yang
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Algebraic Method ◽  
Inverse Kinematic ◽  
New Method ◽  
One Dimension ◽  
Parallel Mechanisms ◽  
Simple Method ◽  
Inverse Kinematics Problem ◽  
Serial Robot

Because the solution to inverse kinematics problem of the general 5R serial robot is unique and its assembly condition has been derived, a simple effective method for inverse kinematics problem of general 6R serial robot or forward kinematics problem of general 7R single-loop mechanism is presented based on one-dimension searching algorithm. The new method has the following features: (1) Using one-dimension searching algorithm, all the real inverse kinematic solutions are obtained and it has higher computing efficiency; (2) Compared with algebraic method, it has evidently reduced the difficulty of deducing formulas. The principle of the new method can be generalized to kinematic analysis of parallel mechanisms.

A Comparison of Architectures of Parallel Mechanisms for Workspace and Kinematic Properties

1995 ◽  
Author(s):  
Clement M. Gosselin ◽  
Rémi Ricard ◽  
Meyer A. Nahon
Keyword(s):  
Parallel Manipulators ◽  
Parallel Architectures ◽  
Parallel Mechanisms ◽  
Design And Optimization ◽  
Stiffness Properties ◽  
Structural Differences ◽  
Six Degree Of Freedom ◽  
Kinematic Properties ◽  
Better Than ◽  
Normalization Factors

Abstract This paper presents a study of the workspace and kinematic properties of four different architectures of six-degree-of-freedom parallel mechanisms. For each architecture, the volume of the Cartesian workspace is computed at different orientations of the moving platform. The distribution of the workspace is also found by computing the 2D sections of the 3D workspace. The rotational workspace is then determined at the reference position of the platform. Finally, the stiffness properties of the architectures are obtained. Normalization factors are then defined to account for the structural differences between the architectures of mechanisms. The comparison of the different architectures of parallel mechanisms has been performed using SIMPA, a specialized CAD tool developed for the kinematic analysis and optimization of parallel manipulators. The results thus obtained illustrate the range of performance which can be expected from different parallel architectures. Although none of the architectures proves to be better than all the others in all respects, particular architectures do excel in particular performance measures. The approach proposed would therefore be useful in further studies relating to the design and optimization of parallel manipulators and mechanisms.

A simple method of polyamine purification

1985 ◽  
Vol 38 (4) ◽  
pp. 633 ◽  
Author(s):  
IW Stapleton
Keyword(s):  
Aqueous Solution ◽  
Anion Exchange ◽  
Large Scale ◽  
Exchange Resin ◽  
Anion Exchange Resin ◽  
Simple Procedure ◽  
Crystalline Solid ◽  
Simple Method

A simple procedure for the large-scale purification of commercial polyethyleneamines (H2N[CH2CH2NH]nH where n = 2-5) is described in which the per- tosylate salt separates as a crystalline solid from aqueous solution. The salts require no further purification except for pentaethylenehexamine (n = 5), which requires recrystallization from water. The free bases are regenerated from the tosylate salt by an anion-exchange resin.

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