Screw System Analysis of Parallel Mechanisms and Applications to Constraint and Mobility Study

2004 ◽  
Author(s):  
Jian S. Dai ◽  
Zhen Huang ◽  
Harvey Lipkin
Keyword(s):  
Degrees Of Freedom ◽  
System Analysis ◽  
General Mechanism ◽  
Parallel Mechanisms ◽  
Mobility Analysis ◽  
New Approach ◽  
Redundant Constraints ◽  
Overconstrained Mechanisms ◽  
Mobility Study ◽  
System Characteristics

The Kutzbach-Gru¨bler mobility criterion calculates the degrees-of-freedom of a general mechanism. However, the criterion can break down for mechanisms with special geometries, and in particular, the class of so-called overconstrained mechanisms. The problem is that the criterion treats all constraints as active, even redundant constraints, which do not affect the mechanism degrees-of-freedom. This paper examines the screw systems of a parallel mechanism to identify the redundant constraints. The screw system characteristics and relationships are then investigated for physical properties. Then a new approach to mobility analysis is proposed based on screw system decompositions. A new version of the mobility criterion is presented to eliminate the redundant constraints and correctly predict the platform degrees-of-freedom. Several examples of overconstrained mechanisms from the literature illustrate the results.

Mobility of Overconstrained Parallel Mechanisms

2004 ◽  
Vol 128 (1) ◽  
pp. 220-229 ◽  
Author(s):  
Jian S. Dai ◽  
Zhen Huang ◽  
Harvey Lipkin
Keyword(s):  
Physical Properties ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
General Mechanism ◽  
Parallel Mechanisms ◽  
Mobility Analysis ◽  
New Approach ◽  
Redundant Constraints ◽  
Overconstrained Mechanisms ◽  
System Characteristics

The Kutzbach–Grübler mobility criterion calculates the degrees of freedom of a general mechanism. However, the criterion can break down for mechanisms with special geometries, and in particular, the class of so-called overconstrained parallel mechanisms. The problem is that the criterion treats all constraints as active, even redundant constraints, which do not affect the mechanism degrees of freedom. In this paper we reveal a number of screw systems of a parallel mechanism, explore their inter-relationship and develop an original theoretical framework to relate these screw systems to motion and constraints of a parallel mechanism to identify the platform constraints, mechanism constraints and redundant constraints. The screw system characteristics and relationships are investigated for physical properties and a new approach to mobility analysis is proposed based on decompositions of motion and constraint screw systems. New versions of the mobility criterion are thus presented to eliminate the redundant constraints and accurately predict the platform degrees of freedom. Several examples of overconstrained mechanisms from the literature illustrate the results.

scholarly journals Screw-System-Based Mobility Analysis of a Family of Fully Translational Parallel Manipulators

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Ernesto Rodriguez-Leal ◽  
Jian S. Dai ◽  
Gordon R. Pennock
Keyword(s):  
System Approach ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
System Analysis ◽  
Parallel Manipulators ◽  
Mobility Analysis ◽  
Redundant Constraints ◽  
The Common

This paper investigates the mobility of a family of fully translational parallel manipulators based on screw system analysis by identifying the common constraint and redundant constraints, providing a case study of this approach. The paper presents the branch motion-screws for the 3-RP̲C-Y parallel manipulator, the 3-RCC-Y (or 3-RP̲RC-Y) parallel manipulator, and a newly proposed 3-RP̲C-T parallel manipulator. Then the paper determines the sets of platform constraint-screws for each of these three manipulators. The constraints exerted on the platforms of the 3-RP̲Carchitectures and the 3-RCC-Y manipulators are analyzed using the screw system approach and have been identified as couples. A similarity has been identified with the axes of couples: they are perpendicular to theRjoint axes, but in the former the axes are coplanar with the base and in the latter the axes are perpendicular to the limb. The remaining couples act about the axis that is normal to the base. The motion-screw system and constraint-screw system analysis leads to the insightful understanding of the mobility of the platform that is then obtained by determining the reciprocal screws to the platform constraint screw sets, resulting in three independent instantaneous translational degrees-of-freedom. To validate the mobility analysis of the three parallel manipulators, the paper includes motion simulations which use a commercially available kinematics software.

Jacobian Derivation of 5-DOF 3R2T Parallel Mechanisms

2004 ◽  
Author(s):  
Qinchuan Li ◽  
Xudong Hu ◽  
Zhen Huang
Keyword(s):  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Kinematic Chain ◽  
Parallel Mechanisms ◽  
Mobility Analysis

This paper presents a method for the Jacobian derivation of 5-DOF 3R2T PMs (parallel mechanisms), where 3R denotes three rotational DOFs (degrees of freedom) and 2T denotes two translational DOFs. First the mobility analysis of such kind of parallel mechanisms is reviewed briefly. The Jacobian matrix of the single limb kinematic chain is obtained via screw theory, which is a 6 × 5 matrix. Then it is shown that the mobility analysis of such kind of PM is important when simplifying the 6 × 5 matrix into a 5 × 5 Jacobian matrix. After obtaining the 5 × 5 Jacobian matrix for each limb, a 5 × 5 Jacobian matrix for the whole mechanism can be established.

Mobility Analysis of a Novel 3-5R Parallel Mechanism Family

2004 ◽  
Vol 126 (1) ◽  
pp. 79-82 ◽  
Author(s):  
Q. C. Li ◽  
Z. Huang
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Kinematic Chain ◽  
Parallel Mechanisms ◽  
Mobility Analysis

Mobility analysis of a novel 3-5R parallel mechanism family whose limb consists of a 2R and a 3R parallel subchain is performed by the aid of screw theory. A mobility criterion applicable to such 3-leg parallel mechanisms in which each kinematic chain contains five kinematic pairs is proposed. It is shown that under different structural conditions, the 3-5R parallel mechanism can have 3, 4, or 5 DOF (degrees of freedom). The structural conditions that guarantee the full-cycle mobility are analyzed. The analysis and the method presented in this paper will be helpful in using such a 3-5R parallel mechanism family and introduce new insights into the mobility analysis of parallel mechanisms.

Mobility Analysis of Limited-Degrees-of-Freedom Parallel Mechanisms in the Framework of Geometric Algebra

2016 ◽  
Vol 8 (4) ◽  
Author(s):  
Qinchuan Li ◽  
Xinxue Chai ◽  
Ji'nan Xiang
Keyword(s):  
Basic Property ◽  
Geometric Algebra ◽  
Degrees Of Freedom ◽  
Linear Equations ◽  
Closed Form Expression ◽  
Parallel Mechanisms ◽  
Motion Pattern ◽  
Mobility Analysis ◽  
Form Expression ◽  
General Method

Mobility is a basic property of a mechanism. The aim of mobility analysis is to determine the number of degrees-of-freedom (DOF) and the motion pattern of a mechanism. The existing methods for mobility analysis have some drawbacks when being applied to limited-DOF parallel mechanisms (PMs). Particularly, it is difficult to obtain a symbolic or closed-form expression of mobility and its geometric interpretations are not always straightforward. This paper presents a general method for mobility analysis of limited-DOF PMs in the framework of geometric algebra. The motion space and constraint space of each limb are expressed using geometric algebra. Then the mobility of the PM can be calculated based on the orthogonal complement relationship between the motion space and the constraint space. The detailed mobility analyses of a 3-RPS PM and a 3-RPC PM are presented. It is shown that this method can obtain a symbolic expression of mobility with straightforward geometric interpretations and is applicable to limited-DOF PMs with or without redundant constraints. Without solving complicated symbolic linear equations, this method also has computational advantages.

Type synthesis of spatial mechanisms for forging manipulators

2012 ◽  
Vol 226 (9) ◽  
pp. 2320-2330 ◽  
Author(s):  
Yundou Xu ◽  
Jiantao Yao ◽  
Yongsheng Zhao
Keyword(s):  
Degrees Of Freedom ◽  
Screw Theory ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Heavy Duty ◽  
Systematic Method ◽  
Type Selection ◽  
Spatial Mechanisms ◽  
Selection For ◽  
Overconstrained Mechanisms

In this study, a systematic method is proposed to synthesize the parallel and hybrid serial–parallel mechanisms for the forging manipulators based on the screw theory. First, several typical configurations of five-degrees-of-freedom parallel mechanism for the forging manipulators are synthesized, and they are all non-overconstrained mechanisms. Then, two kinds of hybrid serial–parallel mechanisms for the forging manipulators with the advantages of motion decoupling are constructed, which are also not overconstrained. The configurations obtained in this study would provide more type selection for the heavy-duty forging manipulators in engineering.

Type Synthesis of Two-Degrees-of-Freedom 3-4R Parallel Mechanisms With Both Spherical Translation Mode and Sphere-on-Sphere Rolling Mode

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Xianwen Kong ◽  
Jingjun Yu
Keyword(s):  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Operation Modes ◽  
The Common ◽  
Moving Platform ◽  
Multiple Operation ◽  
Overconstrained Mechanisms ◽  
Rolling Mode

Parallel manipulators (PMs) with multiple operation modes are novel reconfigurable PMs, which use less number of actuators and can be reconfigured without disassembly. This paper deals with the type synthesis of 2-DOF (degrees-of-freedom) PMs with both spherical translation mode and sphere-on-sphere rolling mode. A spherical translation is the 2-DOF spatial translation under which the trajectory of any point on the moving link is a sphere. A sphere-on-sphere rolling refers to the rolling of a sphere without slipping and spinning on another sphere of the same diameter. At first, a 2-DOF 3-4R overconstrained PM is proposed based on an existing 5-DOF US equivalent PM. From this 2-DOF PM, we further obtain a 3-4R PM for sphere-on-sphere rolling and a 3-4R PM for spherical translation. By finding the common conditions for the 2-DOF 3-4R PM for spherical translation and 2-DOF 3-4R PM for sphere-on-sphere rolling, the types of 2-DOF 3-4R PMs with both spherical translation mode and sphere-on-sphere rolling mode are then obtained. The 2-DOF 3-4R PMs with both spherical translation mode and sphere-on-sphere rolling mode fall into two classes. In one class of PMs with both spherical translation mode and sphere-on-sphere rolling mode, the moving platform has four instantaneous DOF in a transition configuration. In another class of PMs with both spherical translation mode and sphere-on-sphere rolling mode, the moving platform has at most three instantaneous DOF in a transition configuration. This work enriches the types of PMs with multiple operation modes and overconstrained mechanisms.

Scientific-methodological approach to the substantiation of the rational seasonal scenario of using combine harvesters by large-scale agricultural producers

2020 ◽  
pp. 205-217
Author(s):  
V. Skibchyk ◽  
V. Dnes ◽  
R. Kudrynetskyi ◽  
O. Krypuch
Keyword(s):  
Large Scale ◽  
System Analysis ◽  
Methodological Approach ◽  
Production Unit ◽  
Agricultural Producers ◽  
New Approach ◽  
Rational Use ◽  
Road Map ◽  
Analysis And Synthesis ◽  
Combine Harvesters

Аnnotation Purpose. To increase the efficiency of technological processes of grain harvesting by large-scale agricultural producers due to the rational use of combine harvesters available on the farm. Methods. In the course of the research the methods of system analysis and synthesis, induction and deduction, system-factor and system-event approaches, graphic method were used. Results. Characteristic events that occur during the harvesting of grain crops, both within a single production unit and the entire agricultural producer are identified. A method for predicting time intervals of use and downtime of combine harvesters of production units has been developed. The roadmap of substantiation the rational seasonal scenario of the use of grain harvesters of large-scale agricultural producers is developed, which allows estimating the efficiency of each of the scenarios of multivariate placement of grain harvesters on fields taking into account influence of natural production and agrometeorological factors on the efficiency of technological cultures. Conclusions 1. Known scientific and methodological approaches to optimization of machine used in agriculture do not take into account the risks of losses of crops due to late harvesting, as well as seasonal natural and agrometeorological conditions of each production unit of the farmer, which requires a new approach to the rational use of rational seasonal combines of large agricultural producers. 2. The developed new approach to the substantiation of the rational seasonal scenario of the use of combined harvesters of large-scale agricultural producers allows taking into account the costs of harvesting of grain and the cost of the lost crop because of the lateness of harvesting at optimum variants of attraction of additional free combine harvesters. provides more profit. 3. The practical application of the developed road map will allow large-scale agricultural producers to use combine harvesters more efficiently and reduce harvesting costs. Keywords: combine harvesters, use, production divisions, risk, seasonal scenario, large-scale agricultural producers.

scholarly journals A New Approach of Soft Joint Based on a Cable-Driven Parallel Mechanism for Robotic Applications

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1468
Author(s):  
Luis Nagua ◽  
Carlos Relaño ◽  
Concepción A. Monje ◽  
Carlos Balaguer
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Experimental Tests ◽  
Humanoid Robots ◽  
Inverse Kinematic ◽  
Element Analysis ◽  
New Approach ◽  
Flexible Polymer ◽  
The Mathematical Model

A soft joint has been designed and modeled to perform as a robotic joint with 2 Degrees of Freedom (DOF) (inclination and orientation). The joint actuation is based on a Cable-Driven Parallel Mechanism (CDPM). To study its performance in more detail, a test platform has been developed using components that can be manufactured in a 3D printer using a flexible polymer. The mathematical model of the kinematics of the soft joint is developed, which includes a blocking mechanism and the morphology workspace. The model is validated using Finite Element Analysis (FEA) (CAD software). Experimental tests are performed to validate the inverse kinematic model and to show the potential use of the prototype in robotic platforms such as manipulators and humanoid robots.

scholarly journals An automated system analysis and design tool for spacecrafts ceas space journal

2021 ◽  
Author(s):  
Manfred Ehresmann ◽  
Georg Herdrich ◽  
Stefanos Fasoulas
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Degrees Of Freedom ◽  
System Analysis ◽  
Propulsion System ◽  
Optimal System ◽  
Automated System ◽  
Processing Unit ◽  
Data Set ◽  
Analysis And Design

AbstractIn this paper, a generic full-system estimation software tool is introduced and applied to a data set of actual flight missions to derive a heuristic for system composition for mass and power ratios of considered sub-systems. The capability of evolutionary algorithms to analyse and effectively design spacecraft (sub-)systems is shown. After deriving top-level estimates for each spacecraft sub-system based on heuristic heritage data, a detailed component-based system analysis follows. Various degrees of freedom exist for a hardware-based sub-system design; these are to be resolved via an evolutionary algorithm to determine an optimal system configuration. A propulsion system implementation for a small satellite test case will serve as a reference example of the implemented algorithm application. The propulsion system includes thruster, power processing unit, tank, propellant and general power supply system masses and power consumptions. Relevant performance parameters such as desired thrust, effective exhaust velocity, utilised propellant, and the propulsion type are considered as degrees of freedom. An evolutionary algorithm is applied to the propulsion system scaling model to demonstrate that such evolutionary algorithms are capable of bypassing complex multidimensional design optimisation problems. An evolutionary algorithm is an algorithm that uses a heuristic to change input parameters and a defined selection criterion (e.g., mass fraction of the system) on an optimisation function to refine solutions successively. With sufficient generations and, thereby, iterations of design points, local optima are determined. Using mitigation methods and a sufficient number of seed points, a global optimal system configurations can be found.

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