Using a Point-Line-Plane Representation for Unified Simulation of Planar and Spherical Mechanisms

2019 ◽  
Author(s):  
Shashank Sharma ◽  
Anurag Purwar
Keyword(s):  
Geometric Constraints ◽  
Constraint Equations ◽  
Homogeneous Coordinates ◽  
Spatial Mechanisms ◽  
Prismatic Joints ◽  
Spherical Linkages ◽  
Point Line ◽  
Generalized Constraint ◽  
Spherical Mechanism ◽  
Geometric Primitives

Abstract This paper presents a geometric constraints driven approach to unified kinematic simulation of n-bar planar and spherical linkage mechanisms consisting of both revolute and prismatic joints. Generalized constraint equations using point, line and plane coordinates have been proposed which unify simulation of planar and spherical linkages and are demonstrably scalable to spatial mechanisms. As opposed to some of the existing approaches, which seek to derive loop-closure equations for each type of mechanism separately, we have shown that the simulation can be made simpler and more efficient by using unified version of the geometric constraints on joints and links. This is facilitated using homogeneous coordinates and constraints on geometric primitives, such as point, line, and plane. Furthermore, the approach enables simpler programming, real-time computation, and ability to handle any type of planar and spherical mechanism. This work facilitates creation of practical and intuitive design tools for mechanism designers.

Using a Point-Line-Plane Representation for Unified Simulation of Planar and Spherical Mechanisms

2020 ◽  
Vol 20 (6) ◽  
Author(s):  
Shashank Sharma ◽  
Anurag Purwar
Keyword(s):  
Geometric Constraints ◽  
Constraint Equations ◽  
Homogeneous Coordinates ◽  
Spatial Mechanisms ◽  
Prismatic Joints ◽  
Spherical Linkages ◽  
Point Line ◽  
Generalized Constraint ◽  
Spherical Mechanism ◽  
Geometric Primitives

Abstract This paper presents a geometric constraints driven approach to unified kinematic simulation of n-bar planar and spherical linkage mechanisms consisting of both revolute and prismatic joints. Generalized constraint equations using point, line, and plane coordinates have been proposed which unify simulation of planar and spherical linkages and are demonstrably scalable to spatial mechanisms. As opposed to some of the existing approaches, which seek to derive loop-closure equations for each type of mechanism separately, we have shown that the simulation can be made simpler and more efficient by using unified version of the geometric constraints on joints and links. This is facilitated using homogeneous coordinates and constraints on geometric primitives, such as point, line, and plane. Furthermore, the approach enables simpler programming, real-time computation, and ability to handle any type of planar and spherical mechanism. This work facilitates creation of practical and intuitive design tools for mechanism designers.

Assembly Configurations of Spatial Single-Loop Mechanisms With Revolute, Cylindric, and Prismatic Joints

1998 ◽  
Author(s):  
David E. Foster ◽  
Raymond J. Cipra
Keyword(s):  
Single Loop ◽  
Spatial Mechanisms ◽  
Prismatic Joints ◽  
Spherical Mechanism

Abstract This paper examines the problem of identifying the assembly configurations (ACs), also called circuits, of certain spatial single-loop mechanisms. First, the spherical mechanism is considered; it is believed that such a mechanism has one AC if every pair of adjacent links can line up; otherwise, it has 2 ACs. Next, general spatial mechanisms with revolute, cylindric, and prismatic points are considered. If the mechanism has three or more sliding (cylindric or prismatic) joints, it is possible to find an equivalent spherical mechanism which has the same angular motions. However, it is also possible that at certain positions, some of the links may have to slide an infinite distance, which is not possible. Therefore, the mechanism may have more ACs than the equivalent spherical mechanism. Several examples are given, and some general conclusions are drawn.

Computer-Based Kinematical Analysis of Spatial Multiloop Mechanisms

1992 ◽  
Author(s):  
Manfred Hiller ◽  
Manfred Möller
Keyword(s):  
Multibody System ◽  
Nonlinear Constraint ◽  
Constraint Equations ◽  
Revolute Joints ◽  
Spatial Mechanisms ◽  
Joint Coordinates ◽  
Prismatic Joints ◽  
Suitable Structure ◽  
Computer Based ◽  
Spatial Kinematics

Abstract In this paper a method for the automatical analysis of the kinematics of spatial multiloop mechanisms is presented. The mechanism is regarded as a multibody system. Connecting joints are revolute joints (R), prismatic joints (P), spherical joints (S) and all further joints that can be modelled as combinations of these joints. The concept allows the application for a user without deeper theoretical knowledge of spatial kinematics. Special effort has been taken in the reduction of the number of nonlinear constraint equations that must be solved. This is done by using an approach, yielding a suitable structure of the system of nonlinear constraint equations, where only those with interesting unknown joint coordinates must be solved. An optimized solution of these equations allows in many cases a partly and sometimes even a completely explicit solution of the constraint equations. The described method is also applicable to overconstrained spatial mechanisms.

SOLVING SPATIAL CONSTRAINTS WITH GLOBAL DISTANCE COORDINATE SYSTEM

2006 ◽  
Vol 16 (05n06) ◽  
pp. 533-547 ◽  
Author(s):  
LU YANG
Keyword(s):  
Coordinate System ◽  
Systematic Approach ◽  
Distance Geometry ◽  
Spatial Constraints ◽  
Constraint Equations ◽  
System A ◽  
Short Program ◽  
Complete Set ◽  
Point Line ◽  
Made In

A systematic approach making use of distance geometry to solve spatial constraints is introduced. We demonstrate how to create the constraint equations by means of a relevant distance coordinate system. A short program is made (in Maple) which implements the algorithm producing automatically a complete set of constraint equations for a given point-plane configuration. The point-line-plane configurations are converted into point-plane ones beforehand.

Multi-robot system optimization based on redundant serial spherical mechanism for robotic minimally invasive surgery

Robotica ◽  
2018 ◽  
Vol 37 (7) ◽  
pp. 1202-1213 ◽  
Author(s):  
C. A. Nelson ◽  
M. A. Laribi ◽  
S. Zeghloul
Keyword(s):  
Minimally Invasive Surgery ◽  
Minimally Invasive ◽  
Invasive Surgery ◽  
System Optimization ◽  
Design Parameters ◽  
Operating Table ◽  
Robot System ◽  
Spherical Linkages ◽  
Spherical Mechanism ◽  
Multi Robot

SUMMARYSerial spherical linkages have been used in the design of a number of robots for minimally invasive surgery, in order to mechanically constrain the surgical instrument with respect to the incision. However, the typical serial spherical mechanism suffers from conflicting design objectives, resulting in an unsuitable compromise between avoiding collision with the patient and producing good kinematic and workspace characteristics. In this paper, we propose a multi-robot system composed of two redundant serial spherical linkages to achieve this purpose. A multi-objective optimization for achieving the aforementioned design goals is presented first for a single redundant robot and then for a multi-robot system. The problem of mounting multiple robots on the operating table as well as the way cooperative actions can be performed is addressed. The sensitivity of each optimal solution (single-robot and multi-robot) to uncertainties in the design parameters is investigated.

Dynamic Analysis of a Spherical Four Bar Mechanism

1992 ◽  
Author(s):  
J. R. Dooley ◽  
J. M. McCarthy
Keyword(s):  
Equations Of Motion ◽  
Joint Angles ◽  
Euler Parameters ◽  
Generalized Coordinates ◽  
Constraint Equations ◽  
Spherical Mechanisms ◽  
Input And Output ◽  
Closed Chain ◽  
Concentric Spheres ◽  
Spherical Mechanism

Abstract Spherical mechanisms are designed so that the points in each link are constrained to move on concentric spheres This paper develops the equations of motion for spherical four bar mechanisms. While the kinematics of these linkages have been extensively studied, the dynamics equations do not seem to have been previously derived. As design techniques for these mechanisms become more efficient, the equations of motion are required to evaluate their performance. The complete dynamics equations of a four-bar spherical mechanism are derived using the input and output joint angles and the Euler parameters of the coupler as generalized coordinates. These coordinates provide a convenient representation of the constraint equations associated with the closed chain. An example analysis is provided.

Dynamics of Open and Closed Chain Spherical Mechanisms Using Quaternion Coordinates

1992 ◽  
Author(s):  
J. R. Dooley ◽  
J. M. McCarthy
Keyword(s):  
Quadratic Form ◽  
Equations Of Motion ◽  
General Technique ◽  
Quadratic Constraint ◽  
Generalized Coordinates ◽  
Constraint Equations ◽  
Spherical Mechanisms ◽  
Closed Chain ◽  
Spherical Mechanism ◽  
Moving Bodies

Abstract This paper presents a general technique for deriving the equations of motion for any open or closed chain spherical mechanism. The technique uses quaternion coordinates to represent the position of each rigid body in the mechanism. Thus, if there are n moving bodies in the chain, there are 4n generalized coordinates in the equations of motion. The use of quaternion coordinates results in standardized quadratic constraint relations representing the hinged connections between bodies in the mechanism. These constraint equations augment the equations of motion. This technique has two important features. First, it is specifically adapted to spherical mechanisms and presents all positions as rotations. Second, the quadratic form of the constraint equations simplifies the computation of velocities and accelerations compatible with the constraints. As an example the equations of motion for a closed six bar spherical chain are derived.

Checking Geometric Constraints in Layout Design Using Primitives

1996 ◽  
Author(s):  
H. Yim ◽  
A. C. Butler
Keyword(s):  
Computational Efficiency ◽  
Layout Design ◽  
Geometric Constraints ◽  
Parallel Computer ◽  
Test Problems ◽  
Constraint Checking ◽  
Level Of Abstraction ◽  
Computational Speed ◽  
Geometric Primitives ◽  
New Algorithms

Abstract The use of geometric primitives provides representation of objects in layout design at an appropriate level of abstraction, and it allows the use of two new algorithms which permit improvements in computational speed for constraint checking. These algorithms detect intersections between two rectangles and between a rectangle and circle with improved computational efficiency. The use of this pair of algorithms is demonstrated on test problems executed on a parallel computer, and conclusions are drawn regarding the use of geometric primitives for constraint checking in layout design.

Complete 3D boundary representation from multiple range images: exploiting geometric constraints

Robotica ◽  
1995 ◽  
Vol 13 (4) ◽  
pp. 339-349
Author(s):  
Kamal Gupta ◽  
Zukang Xu
Keyword(s):  
Boundary Representation ◽  
Geometric Constraints ◽  
Range Images ◽  
Noise Levels ◽  
Object A ◽  
3 Dimensional ◽  
Local View ◽  
Merging Process ◽  
The Face ◽  
Geometric Primitives

SummaryWe describe an approach that generates a complete b-rep description of a polyhedral object from (geometric primitives derived from) dense range images taken from multiple view-points. Our approach, starting from basic face models of visible surfaces of objects in each local view, matches certain geometric features, extracts rigid-body transformations that relate the local views, and incrementally merges the face models (in local views) into a global 3-dimensional b-rep description of the object. A convenient and effective termination criterion is designed to monitor the merging process. The emphasis is on the use of geometric constraints in building a complete 3-dimensional model of the object.We have implemented this system in C, running on a SUN Sparcstation. The system, as presented, has been tested on face models derived from several synthetic and real range images and performs successfully with realistic noise levels.

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.

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