Position-Force Synthesis of Closed-Loop Linkages

1994 ◽  
Vol 116 (1) ◽  
pp. 155-162 ◽  
Author(s):  
C. Huang ◽  
B. Roth
Keyword(s):  
Linear Algebra ◽  
Closed Loop ◽  
Screw Theory ◽  
Dimensional Synthesis ◽  
Position Synthesis

The dimensional synthesis of spatial closed-loop linkages to match both force and position specifications is investigated. An efficient means of formulating force equations is introduced through the application of linear algebra to screw theory. The synthesis of spatial four-bar linkages is discussed in detail; it is shown that the maximum number of allowable design positions is not decreased after force constraints are imposed on classical position synthesis problems.

Position-Force Synthesis of Closed-Loop Linkages

1992 ◽  
Author(s):  
Chintien Huang ◽  
Bernard Roth
Keyword(s):  
Linear Algebra ◽  
Closed Loop ◽  
Screw Theory ◽  
Dimensional Synthesis ◽  
Position Synthesis

Abstract The dimensional synthesis of spatial closed-loop linkages to match both force and position specifications is investigated. An efficient means of formulating force equations is introduced through the application of linear algebra to screw theory. The synthesis of spatial four-bar linkages is discussed in detail; it is shown that the maximum number of allowable design positions is not decreased after force constraints are imposed on classical position synthesis problems.

scholarly journals A New Method for Type Synthesis of 2R1T and 2T1R 3-DOF Redundant Actuated Parallel Mechanisms with Closed Loop Units

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Yongquan Li ◽  
Yang Zhang ◽  
Lijie Zhang
Keyword(s):  
Closed Loop ◽  
Screw Theory ◽  
Line Graph ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Allocation Criteria ◽  
Grassmann Line Geometry ◽  
Moving Platform ◽  
Atlas Method

Abstract The current type synthesis of the redundant actuated parallel mechanisms is adding active-actuated kinematic branches on the basis of the traditional parallel mechanisms, or using screw theory to perform multiple getting intersection and union to complete type synthesis. The number of redundant parallel mechanisms obtained by these two methods is limited. In this paper, based on Grassmann line geometry and Atlas method, a novel and effective method for type synthesis of redundant actuated parallel mechanisms (PMs) with closed-loop units is proposed. Firstly, the degree of freedom (DOF) and constraint line graph of the moving platform are determined successively, and redundant lines are added in constraint line graph to obtain the redundant constraint line graph and their equivalent line graph, and a branch constraint allocation scheme is formulated based on the allocation criteria. Secondly, a scheme is selected and redundant lines are added in the branch chains DOF graph to construct the redundant actuated branch chains with closed-loop units. Finally, the branch chains that meet the requirements of branch chains configuration criteria and F&C (degree of freedom & constraint) line graph are assembled. In this paper, two types of 2 rotational and 1 translational (2R1T) redundant actuated parallel mechanisms and one type of 2 translational and 1 rotational (2T1R) redundant actuated parallel mechanisms with few branches and closed-loop units were taken as examples, and 238, 92 and 15 new configurations were synthesized. All the mechanisms contain closed-loop units, and the mechanisms and the actuators both have good symmetry. Therefore, all the mechanisms have excellent comprehensive performance, in which the two rotational DOFs of the moving platform of 2R1T redundant actuated parallel mechanism can be independently controlled. The instantaneous analysis shows that all mechanisms are not instantaneous, which proves the feasibility and practicability of the method.

Workspace, dexterity and dimensional optimization of microhexapod

2015 ◽  
Vol 35 (4) ◽  
pp. 341-347 ◽  
Author(s):  
E. Rouhani ◽  
M. J. Nategh
Keyword(s):  
Degrees Of Freedom ◽  
Optimization Problem ◽  
Screw Theory ◽  
Design Parameters ◽  
Dimensional Synthesis ◽  
Content Type ◽  
Workspace Analysis ◽  
The Difference ◽  
Flexure Joints ◽  
6 Degrees Of Freedom

Purpose – The purpose of this paper is to study the workspace and dexterity of a microhexapod which is a 6-degrees of freedom (DOF) parallel compliant manipulator, and also to investigate its dimensional synthesis to maximize the workspace and the global dexterity index at the same time. Microassembly is so essential in the current industry for manufacturing complicated structures. Most of the micromanipulators suffer from their restricted workspace because of using flexure joints compared to the conventional ones. In addition, the controllability of micromanipulators inside the whole workspace is very vital. Thus, it is very important to select the design parameters in a way that not only maximize the workspace but also its global dexterity index. Design/methodology/approach – Microassembly is so essential in the current industry for manufacturing complicated structures. Most of the micromanipulators suffer from their restricted workspace because of using flexure joints compared to the conventional ones. In addition, the controllability of micromanipulators inside the whole workspace is very vital. Thus, it is very important to select the design parameters in a way that not only maximize the workspace but also its global dexterity index. Findings – It has been shown that the proposed procedure for the workspace calculation can considerably speed the required calculations. The optimization results show that a converged-diverged configuration of pods and an increase in the difference between the moving and the stationary platforms’ radii cause the global dexterity index to increase and the workspace to decrease. Originality/value – The proposed algorithm for the workspace analysis is very important, especially when it is an objective function of an optimization problem based on the search method. In addition, using screw theory can simply construct the homogeneous Jacobian matrix. The proposed methodology can be used for any other micromanipulator.

Designing Planar Mechanisms Using a Bi-Invariant Metric in the Image Space of SO (3)

1994 ◽  
Author(s):  
Pierre Larochelle ◽  
J. Michael McCarthy
Keyword(s):  
Rigid Body ◽  
Numerical Results ◽  
Image Space ◽  
Dimensional Synthesis ◽  
Invariant Metric ◽  
Planar Mechanisms ◽  
Position And Orientation ◽  
Position Synthesis

Abstract In this paper we present a technique for using a bi-invariant metric in the image space of spherical displacements for designing planar mechanisms for n (> 5) position rigid body guidance. The goal is to perform the dimensional synthesis of the mechanism such that the distance between the position and orientation of the guided body to each of the n goal positions is minimized. Rather than measure these distances in the plane, we introduce an approximating sphere and identify rotations which are equivalent to the planar displacements to a specified tolerance. We then measure distances between the rigid body and the goal positions using a bi-invariant metric on the image space of SO(3). The optimal linkage is obtained by minimizing this distance over all of the n goal positions. The paper proceeds as follows. First, we approximate planar rigid body displacements with spherical displacements and show that the error induced by such an approximation is of order 1/R2, where R is the radius of the approximating sphere. Second, we use a bi-invariant metric in the image space of spherical displacements to synthesize an optimal spherical 4R mechanism. Finally, we identify the planar 4R mechanism associated with the optimal spherical solution. The result is a planar 4R mechanism that has been optimized for n position rigid body guidance using an approximate bi-invariant metric with an error dependent only upon the radius of the approximating sphere. Numerical results for ten position synthesis of a planar 4R mechanism are presented.

Dimensional Synthesis of a Novel 2T2R Parallel Manipulator for Medical Applications

2014 ◽  
Author(s):  
Nitish Kumar ◽  
Olivier Piccin ◽  
Bernard Bayle
Keyword(s):  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Screw Theory ◽  
Structural Parameters ◽  
Geometric Analysis ◽  
Medical Applications ◽  
Dimensional Synthesis ◽  
Synthesis Algorithm ◽  
Percutaneous Procedures ◽  
Actuated Joints

This paper deals with the dimensional synthesis of a novel parallel manipulator for medical applications. This parallel mechanism has a novel 2T2R mobility derived from the targeted application of needle manipulation. The kinematic design of this 2T2R manipulator and its novelty are illustrated in relation to the percutaneous procedures. Due to the demanding constraints on its size and compactness, achieving a large workspace especially in orientation, is a rather difficult task. The workspace size and kinematic constraint analysis are considered for the dimensional synthesis of this 2T2R parallel mechanism. A dimensional synthesis algorithm based on the screw theory and the geometric analysis of the singularities is described. This algorithm also helps to eliminate the existence of voids inside the workspace. The selection of the actuated joints is validated. Finally, the dimensions of the structural parameters of the mechanism are calculated for achieving the required workspace within the design constraints of size, compactness and a preliminary prototype without actuators is presented.

Singularity Analysis of a Novel 4-DOFs Parallel Robot H4 by Using Screw Theory

2003 ◽  
Author(s):  
Hee-Byoung Choi ◽  
Atsushi Konno ◽  
Masaru Uchiyama
Keyword(s):  
Closed Loop ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
Loop Structure ◽  
Singular Configurations ◽  
Planning And Control ◽  
Kinematic Singularities ◽  
And Control

The closed-loop structure of a parallel robot results in complex kinematic singularities in the workspace. Singularity analysis become important in design, motion, planning, and control of parallel robot. The traditional method to determine a singular configurations is to find the determinant of the Jacobian matrix. However, the Jacobian matrix of a parallel manipulator is complex in general, and thus it is not easy to find the determinant of the Jacobian matrix. In this paper, we focus on the singularity analysis of a novel 4-DOFs parallel robot H4 based on screw theory. Two types singularities, i.e., the forward and inverse singularities, have been identified.

scholarly journals Type Synthesis of 3-Translational Redundant Actuated Parallel Mechanisms With Closed-Loop Branch Chains Based On Graphical Approach

2021 ◽  
Author(s):  
Yongquan Li ◽  
Hong-Sheng Jiang ◽  
Tian-Yu Zheng ◽  
Ke-Long Xi ◽  
Han Jing ◽  
...  
Keyword(s):  
Bearing Capacity ◽  
Parallel Mechanism ◽  
Large Scale ◽  
Vibration Isolation ◽  
Closed Loop ◽  
Screw Theory ◽  
Simple Calculation ◽  
Parallel Mechanisms ◽  
Logistics Industry ◽  
Graphical Approach

Abstract The 3-translational parallel mechanism is widely used in industrial, medical, and military fields, among others. With the development of the national logistics industry, a pressing need for a kind of 3-translational parallel mechanism emerged. Such mechanisms have high stiffness and high bearing capacity and are used for cargo handling and sorting. A novel method based on the graphical approach was proposed for the synthesis of 3-translational redundancy actuated parallel mechanism with closed-loop branch chains. The new mechanism has four symmetrically arranged branch chains, which eases subsequent kinematics and dynamics analyses while providing good mechanical properties. Based on the graphical approach theory, according to the constraint number contained in the branch chain, two types of redundant driven branch chains with closed-loop structures were constructed. The first type includes rotation constraint in one direction, while the second type includes the rotation constraint in two directions. Based on various combinations of two branch chain types, their allocation schemes can be divided into two types. Moreover, said these two allocation schemes can be integrated into at least 500 and 400 types of 3-translational redundant actuated parallel mechanisms with closed-loop branch chains. Then, the degree of freedom properties of representative mechanisms were tested using the screw theory. A large number of novel mechanisms were integrated assessed using this method, and branch chains such mechanisms were symmetrically distributed. They have a strong bearing capacity, simple calculation, and control, and can be applied to the handling and sorting of goods, large-scale precision machine tools, and large construction machinery vibration isolation systems, among others.

Design of a Bistable Origami Reverse-Fold Using Spherical Kinematics

2017 ◽  
Author(s):  
Rami Alfattani ◽  
Craig Lusk
Keyword(s):  
Change Point ◽  
Design Concept ◽  
Dimensional Synthesis ◽  
Bistable Behavior ◽  
Spherical Mechanisms ◽  
Formal Analogy ◽  
Simple Class ◽  
Parametric Cad ◽  
Position Synthesis ◽  
Spherical Mechanism

This paper presents a new design concept for bistability that can be implemented as a reverse-fold origami mechanism or as a spherical four-bar mechanism. The design is based on the conceptual overlap between a certain simple class of origami mechanisms (the reverse-fold) and a class of spherical change-point mechanisms. Using both a partially compliant spherical mechanism and a piece of origami made with two sheets of paper, we implement the design concept for bistable behavior. The design concept consists in adapting planar two position synthesis to spherical mechanisms and in using a formal analogy between spherical mechanisms and certain simple origami folds. The dimensional synthesis of these two mechanisms is performed using parametric CAD. The design concept was successfully prototyped both as origami and as a partially compliant spherical mechanism.

Motion/Force Transmission Analysis of Parallel Mechanisms With Planar Closed-Loop Subchains

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
Kristan Marlow ◽  
Mats Isaksson ◽  
Jian S. Dai ◽  
Saeid Nahavandi
Keyword(s):  
Performance Measures ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Closed Loop ◽  
Screw Theory ◽  
Parallel Mechanisms ◽  
Force Transmission ◽  
Six Degrees Of Freedom ◽  
Lower Mobility ◽  
Transmission Ability

Singularities are one of the most important issues affecting the performance of parallel mechanisms. A parallel mechanism with less than six degrees of freedom (6DOF) is classed as having lower mobility. In addition to input–output singularities, such mechanisms potentially suffer from singularities among their constraints. Furthermore, the utilization of closed-loop subchains (CLSCs) may introduce additional singularities, which can strongly affect the motion/force transmission ability of the entire mechanism. In this paper, we propose a technique for the analysis of singularities occurring within planar CLSCs, along with a finite, dimensionless, frame invariant index, based on screw theory, for examining the closeness to these singularities. The integration of the proposed index with existing performance measures is discussed in detail and exemplified on a prototype industrial parallel mechanism.

Multi-position Dimensional Synthesis of a Spatial 3-RPS Parallel Manipulator

2005 ◽  
Vol 128 (4) ◽  
pp. 815-819 ◽  
Author(s):  
Nalluri Mohan Rao ◽  
K. Mallikarjuna Rao
Keyword(s):  
Approximation Method ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Least Square ◽  
Dimensional Synthesis ◽  
Modified Method ◽  
Moving Platform ◽  
Position Synthesis

This paper presents dimensional synthesis of a 3 degrees of freedom (DOF) spatial 3-revolute-prismatic-spherical (RPS) parallel manipulator. Tsai and Kim ((2003) ASME J. Mech. Des., 125, pp. 92–97) have shown that the dimensional synthesis can be carried out for at the most six prescribed positions and orientations of the moving platform. The method of synthesis is modified (least-square technique) to make it possible to synthesize the 3-RPS manipulator for any number of positions and orientations of the moving platform. The effectiveness of the modified method of synthesis is demonstrated by considering an example for ten-position synthesis. The modified method of synthesis is an approximation method.

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