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.

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.

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.

Fine-Tuning Geometrically Constrained Planar Motions

2011 ◽  
Author(s):  
Ping Zhao ◽  
Q. J. Ge ◽  
Feng Gao ◽  
Hai-Jun Su
Keyword(s):  
Standard Deviation ◽  
Kinetic Energy ◽  
Reference Frames ◽  
Distance Measure ◽  
Fine Tuning ◽  
Planar Motion ◽  
Motion Error ◽  
Point Trajectories ◽  
Geometrically Constrained ◽  
Planar Motions

This paper presents a method for fine-tuning a geometrically constrained planar motion in the context of motion approximation. It builds on the recent work that seeks to identify and extract point trajectories of an explicitly given planar motion. Once two point trajectories are obtained, the remaining issue is to determine the length of the “coupler link” that connects the two point trajectories such that the resulting motion best approximates the original motion. In this paper, the concept of standard deviation in statistics and probability theory is used to define the “distance” between two planar motions. This distance definition is bi-invariant with respect to the choice of both moving and fixed reference frames. Furthermore, the concept of kinetic energy is also used for combining translation with rotation when calculating the distance between two planar displacements. A simple, direct search method for obtaining the optimum length of the coupler link is presented that minimizes the standard deviation of the motion error in terms of the kinetic energy based distance measure for planar displacements.

Bobillier Formula for One Parameter Motions in the Complex Plane

2012 ◽  
Vol 4 (2) ◽  
Author(s):  
Soley Ersoy ◽  
Nurten Bayrak
Keyword(s):  
Complex Plane ◽  
Complex Number ◽  
Second Order ◽  
Geometrical Interpretation ◽  
Planar Motion ◽  
Radius Of Curvature ◽  
Fundamental Law ◽  
Planar Motions

This is a brief note expanding on the aspect of Fayet (2002, “Bobillier Formula as a Fundamental Law in Planar Motion,” Z. Angew. Math. Mech., 82(3), pp. 207–210), which investigates the Bobillier formula by considering the properties up to the second order planar motion. In this note, the complex number forms of the Euler Savary formula for the radius of curvature of the trajectory of a point in the moving complex plane during one parameter planar motion are taken into consideration and using the geometrical interpretation of the Euler Savary formula, Bobillier formula is established for one parameter planar motions in the complex plane. Moreover, a direct way is chosen to obtain Bobillier formula without using the Euler Savary formula in the complex plane. As a consequence, the Euler Savary given in the complex plane will appear as a particular case of Bobillier formula.

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.

scholarly journals Patrones de desplazamiento del eje instantáneo de rotación del movimiento de elevación humeral

2019 ◽  
Author(s):  
Álvaro Felipe Page ◽  
Magda Liliana Cáceres Cáceres
Keyword(s):  
Degree Of Freedom ◽  
Planar Motion ◽  
Helical Axis ◽  
Optimal Average ◽  
Planar Motions

En este trabajo se presentan los resultados de un estudio experimental para la descripción de las trayectorias descritas por el eje instantáneo de rotación (EIR) toracohumeral para movimientos cíclicos de elevación-descenso. Se ha desarrollado una técnica de análisis de movimientos mediante videofotogrametría que permite la medida del EIR del movimiento relativo húmero tórax con un error inferior a 1 cm y de forma muy reproducible [1,2]. Esto permite registrar el movimiento continuo del EIR como un axoide, cuyo desplazamiento mediolateral está relacionado con las velocidades de rotación de las articulaciones esternoclavicular, acromioclavicular y glenohumeral, y cuya posición vertical se asocia a la elevación de articulación glenohumeral [3] Se ha realizado un estudio con 45 sujetos sanos y 15 sujetos con patologías del hombro, analizando el movimiento cíclico de elevación-descenso del húmero en los planos frontal y escapular. La ubicación y forma de los axoides es sensible a los efectos de la carga y del estado funcional del sujeto. Así el efecto de la carga se manifiesta en un desplazamiento medial de la trayectoria del EIR, asociado a un movimiento más acusado de las articulaciones esternoclavicular, acromioclavicular frente al movimiento sin carga. Por otra parte, el efecto de la patología afecta a la trayectoria del EIR sólo a partir de cierto nivel de limitación funcional. Los patrones correspondientes a pacientes con limitaciones leves no muestran diferencias importantes frente a los sujetos sanos. Los resultados obtenidos muestran que el EIR puede ser de utilidad en la valoración funcional biomecánica del hombro, al ofrecer información sobre la coordinación de las diferentes articulaciones que lo constituyen REFERENCIAS [1]  A.Page, J.A. Gálvez, H. de Rosario, V. Mata., J. Prat. Optimal average path of the instantaneous shelical axis in planar motions with one functional degree of freedom. Jnl. Biomech, vol. 43, pp 375-378, 2010. doi: 10.1016/j.jbiomech.2009.09.023. [2]  A.Page, H. de Rosario, J.A. Gálvez, V. Mata. Representation of planar motion of complex joints by means of rolling pairs. Application to neck motion. Jnl. Biomech, vol. 44, pp 747-750, 2011. doi: 10.1016/j.jbiomech.2010.11.019. [3]  M. Cáceres, P. Serra, J. Lopez, & A. Page. Reliability of the Shoulder Instantaneous Helical Axis measurement during the scaption movement. Gait & Posture, vol. 49, pp 268, 2016.

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.

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.

Kinematic Mappings. Part 1: Classification of Algebraic Motions in the Plane

1981 ◽  
Vol 103 (3) ◽  
pp. 585-591 ◽  
Author(s):  
S. De Sa ◽  
B. Roth
Keyword(s):  
Classification Scheme ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Planar Motion ◽  
Rotation Curves ◽  
Planar Motions ◽  
Three Dimensional Space

A classification scheme is developed for algebraic motions in the plane. The method is based upon the study of curves in a special three dimensional space into which the planar motions are mapped. As an example all possible cubic motions are classified. It is shown that this mapping, originally proposed by Blaschke, is based upon the rotation curves and the rotation angles of the planar motion.

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