scholarly journals A Line Geometric Approach to Kinematic Acquisition of Geometric Constraints of Planar Motion

2017 ◽  
Vol 9 (4) ◽  
Author(s):  
Jun Wu ◽  
Xiangyun Li ◽  
Q. J. Ge ◽  
Feng Gao ◽  
Xueyin Liu
Keyword(s):  
Geometric Approach ◽  
Geometric Constraints ◽  
Planar Motion ◽  
Constrained Motion ◽  
Discrete Form ◽  
Mechanical Linkage

This paper examines the problem of geometric constraints acquisition of planar motion through a line-geometric approach. In previous work, we have investigated the problem of identifying point-geometric constraints associated with a motion task which is given in a parametric or discrete form. In this paper, we seek to extend the point-centric approach to the line-centric approach. The extracted geometric constraints can be used directly for determining the type and dimensions of a physical device such as mechanical linkage that generates this constrained motion task.

Kinematic Acquisition of Geometric Constraints for Task Centered Mechanism Design

2010 ◽  
Author(s):  
Jun Wu ◽  
Q. J. Ge ◽  
Hai-Jun Su ◽  
Feng Gao
Keyword(s):  
Mechanism Design ◽  
Motion Analysis ◽  
Geometric Constraints ◽  
Planar Motion ◽  
Dimensional Synthesis ◽  
Constrained Motion ◽  
Analysis Problem ◽  
Geometric Means ◽  
New Type ◽  
Mechanical Linkage

A motion task can be given in various ways. It may be defined parametrically or discretely in terms of an ordered sequence of displacements or in geometric means. This paper studies a new type of motion analysis problem in planar kinematics that seeks to acquire geometric constraints associated with a planar motion task which is given either parametrically or discretely. The resulting geometric constraints can be used directly for type as well as dimensional synthesis of a physical device such as mechanical linkage that generates the constrained motion task. Methods for kinematic acquisition of geometric constraints bridge the gap between type and dimensional synthesis and provide the foundation for task centered mechanism design.

A Line Geometric Approach to Kinematic Acquisition of Geometric Constraints

2012 ◽  
Author(s):  
Jun Wu ◽  
Q. J. Ge ◽  
Feng Gao
Keyword(s):  
Geometric Approach ◽  
Geometric Constraints ◽  
Planar Motion ◽  
Planar Motions

This paper deals with the problem of geometrically defined planar motions using a line geometric approach. In a previous work, we have studied the problem of acquiring geometric constraints associated with a planar motion task using point geometric constraints. This paper extends this work from point geometric domain to line geometric domain.

Kinematic Acquisition of Geometric Constraints for Task-Oriented Design of Planar Mechanisms

2012 ◽  
Vol 5 (1) ◽  
Author(s):  
Jun Wu ◽  
Q. J. Ge ◽  
Hai-Jun Su ◽  
Feng Gao
Keyword(s):  
Mechanism Design ◽  
Geometric Constraints ◽  
Dimensional Synthesis ◽  
Constrained Motion ◽  
Planar Mechanisms ◽  
Analysis Problem ◽  
Geometric Means ◽  
New Type ◽  
Mechanical Linkage ◽  
Task Oriented

A motion task can be given in various ways. It may be defined parametrically or discretely in terms of an ordered sequence of displacements or in geometric means. This paper studies a new type of motion analysis problem in planar kinematics that seeks to acquire geometric constraints associated with a planar motion task which is given either parametrically or discretely. The resulting geometric constraints can be used directly for type as well as dimensional synthesis of a physical device such as mechanical linkage that generates the constrained motion task. Examples are provided toward the end of the paper to illustrate how geometric constraints acquired can be used for task-oriented mechanism design.

Constraint-Based Virtual Environment for Supporting Assembly and Maintainability Tasks

1999 ◽  
Author(s):  
Terrence Fernando ◽  
Prasad Wimalaratne ◽  
Kevin Tan
Keyword(s):  
Virtual Environment ◽  
Current System ◽  
Research Programme ◽  
Geometric Constraints ◽  
Simulation Environment ◽  
Constrained Motion ◽  
Constraint Management ◽  
Interactive Product ◽  
Assembly Operations ◽  
The University

Abstract This paper presents the design and implementation of a constraint-based virtual environment for supporting interactive assembly and maintenance tasks. The system architecture of the constraint-based virtual environment is based on the integration of components such as OpenGL Optimizer, Parasolid geometric kernel, a Constraint Engine and an Assembly Relationship Graph (ARG). The approach presented in this paper is based on pure geometric constraints. Techniques such as automatic constraint recognition, constraint satisfaction, constraint management and constrained motion are employed to support interactive assembly operations and realistic behaviour of assembly parts. The current system has been evaluated using two industrial case studies. This work is being carried out as a part of a research programme referred to as IPSEAM (Interactive Product Simulation Environment for Assessing Assembly and Maintainability), at the University of Salford.

Synthesis and Analysis of 4-DOF Parallel Manipulators of Computer Aided Geometry Approach

2014 ◽  
Vol 912-914 ◽  
pp. 1010-1016
Author(s):  
Yan Hua Zhang ◽  
Xiu Ju Du ◽  
Bai Yong Zhang
Keyword(s):  
Computer Simulation ◽  
Kinematic Analysis ◽  
Geometric Approach ◽  
Parallel Manipulators ◽  
Geometric Constraints ◽  
Type Synthesis ◽  
Moving Platforms ◽  
Kinematic Characteristics ◽  
Computer Aided

A novel computer aided geometry approach for type synthesis and analysis of new spatial 4-DOF parallel manipulators is put forward, and create the computer simulation mechanisms of parallel manipulators using the geometric constraints and dimension driving techniques in CAD software, Based on the computer simulation mechanisms of parallel manipulators, several new spatial 4-DOF parallel manipulators are synthesized, the kinematic characteristics of the moving platforms are analyzed by computer simulation. The results of computer simulation prove that the computer aided geometric approach for solving type synthesis and kinematic analysis is not only fairly quick and straightforward, but also has the advantages of accuracy.

CONTROL OF A COMPLIANT HUMANOID ROBOT IN DOUBLE SUPPORT PHASE: A GEOMETRIC APPROACH

2012 ◽  
Vol 09 (01) ◽  
pp. 1250004 ◽  
Author(s):  
GUSTAVO MEDRANO CERDA ◽  
HOUMAN DALLALI ◽  
MARTIN BROWN
Keyword(s):  
Energy Efficiency ◽  
Degrees Of Freedom ◽  
Geometric Approach ◽  
Research Problem ◽  
Bipedal Walking ◽  
Constrained Motion ◽  
Double Support ◽  
Compliant Actuators ◽  
Support Phase ◽  
Double Support Phase

Enhancing energy efficiency of bipedal walking is an important research problem that has been approached by design of recently developed compliant bipedal robots such as CoMan. While compliance leads to energy efficiency, it also complicates the walking control system due to further under-actuated degrees of freedom (DoF) associated with the compliant actuators. This problem becomes more challenging as the constrained motion of the robot in double support is considered. In this paper this problem is approached from a multi-variable geometric control aspect to systematically account for the compliant actuators dynamics and constrained motion of the robot in double support phase using a detailed electro-mechanical model of CoMan. It is shown that the formulation of constraint subspace is non-trivial in the case of non-rigid robots. A step-wise numerical algorithm is provided and the effectiveness of the proposed method is illustrated via simulation, using a ten DoF model of CoMan.

A Computational Geometric Approach for Motion Generation of Spatial Linkages With Sphere and Plane Constraints

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Xiangyun Li ◽  
Q. J. Ge ◽  
Feng Gao
Keyword(s):  
Geometric Approach ◽  
Geometric Constraints ◽  
Dimensional Synthesis ◽  
Motion Generation ◽  
Geometric Framework ◽  
Kinematic Chains ◽  
Kinematic Mapping ◽  
Spherical Linkages ◽  
Spatial Displacements ◽  
The Given

This paper studies the problem of spatial linkage synthesis for motion generation from the perspective of extracting geometric constraints from a set of specified spatial displacements. In previous work, we have developed a computational geometric framework for integrated type and dimensional synthesis of planar and spherical linkages, the main feature of which is to extract the mechanically realizable geometric constraints from task positions, and thus reduce the motion synthesis problem to that of identifying kinematic dyads and triads associated with the resulting geometric constraints. The proposed approach herein extends this data-driven paradigm to spatial cases, with the focus on acquiring the point-on-a-sphere and point-on-a-plane geometric constraints which are associated with those spatial kinematic chains commonly encountered in spatial mechanism design. Using the theory of kinematic mapping and dual quaternions, we develop a unified version of design equations that represents both types of geometric constraints, and present a simple and efficient algorithm for uncovering them from the given motion.

Task constrained motion planning for 7-degree of freedom manipulators with parameterized submanifolds

2018 ◽  
Vol 45 (3) ◽  
pp. 363-370 ◽  
Author(s):  
Qiang Qiu ◽  
Qixin Cao
Keyword(s):  
Motion Planning ◽  
Explicit Expression ◽  
Collision Detection ◽  
Tool Path ◽  
Degree Of Freedom ◽  
Geometric Constraints ◽  
Constrained Motion ◽  
Content Type ◽  
Planning Methods ◽  
Two Parameters

PurposeThis paper aims to use the redundancy of a 7-DOF (degree of freedom) serial manipulator to solve motion planning problems along a given 6D Cartesian tool path, in the presence of geometric constraints, namely, obstacles and joint limits.Design/methodology/approachThis paper describes an explicit expression of the task submanifolds for a 7-DOF redundant robot, and the submanifolds can be parameterized by two parameters with this explicit expression. Therefore, the global search method can find the feasible path on this parameterized graph.FindingsThe proposed planning algorithm is resolution complete and resolution optimal for 7-DOF manipulators, and the planned path can satisfy task constraint as well as avoiding singularity and collision. The experiments on Motoman SDA robot are reported to show the effectiveness.Research limitations/implicationsThis algorithm is still time-consuming, and it can be improved by applying parallel collision detection method or lazy collision detection, adopting new constraints and implementing more effective graph search algorithms.Originality/valueCompared with other task constrained planning methods, the proposed algorithm archives better performance. This method finds the explicit expression of the two-dimensional task sub-manifolds, so it’s resolution complete and resolution optimal.

The Geometric Generation of the Joint Loci of Spatial Dyads With Axis Joints

1992 ◽  
Author(s):  
J. Keith Nisbett ◽  
T. J. Lawley
Keyword(s):  
General Procedure ◽  
Analytical Techniques ◽  
Geometric Approach ◽  
Geometric Constraints ◽  
Geometric Constraint ◽  
Physical Linkage ◽  
Four Bar Linkage ◽  
Linkage Synthesis

Abstract The geometric aspects of Burmester theory, as used in planar four-bar linkage synthesis, are examined to define a general procedure which is applied to the generation of the joint loci of spatial dyads with axis joints. The joints are geometrically related to the screw axes of the prescribed motion, by means of a screw triangle. The geometric relationships are typically separated into several geometric constraints. Each geometric constraint is considered separately to generate the loci of lines representing joint axes which satisfy the constraint. Combining the loci from each constraint produces a single loci of all the possible fixed or moving joints. The geometric approach is shown to have several benefits not obtained in numerical and pure analytical techniques, especially in relating the characteristics of the loci to the physical linkage and its required motion.

Rational Motion Interpolation Under Kinematic Constraints of Planar 6R Closed Chain

2007 ◽  
Author(s):  
Zhe Jin ◽  
Q. J. Ge
Keyword(s):  
Rational Interpolation ◽  
Geometric Constraints ◽  
Rational Curve ◽  
Constrained Motion ◽  
Extreme Position ◽  
Kinematic Constraints ◽  
Closed Chain ◽  
Curve Interpolation

This paper deals with the problem of synthesizing planar rational motions under the kinematic constraints of planar 6R closed chain. It follows our previous work on the synthesis of rational motions under the kinematic constraints of planar open chains. Planar quaternions are used to represent planar displacements. In this way, the problem of rational motion interpolation is transformed into that of rational curve interpolation, and the kinematic constraints of a planar 6R closed chain are transformed into geometric constraints for the rational interpolation. An algorithm for the constrained motion interpolation is developed that detects an extreme position on the rational motion that violates the kinematic constraints. This position is then modified so that it is in compliance with the kinematic constraints and is added to the list of positions to be interpolated. By restricting the kinematic constraints to 5R and 4R closed chains, the algorithm is also applicable to the problem of synthesizing planar rational motions for 5R and 4R closed chains.

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