Closed Form Displacement Relationships of Single and Multi-Loop Six-Link Spatial Mechanisms

1973 ◽  
Vol 95 (3) ◽  
pp. 709-716 ◽  
Author(s):  
A. H. Soni ◽  
R. V. Dukkipati ◽  
M. Huang
Keyword(s):  
Closed Form ◽  
Single Loop ◽  
Spatial Mechanisms

Using (3 × 3) matrices with dual elements, two loop Watt and Stephenson type six-link spatial mechanisms with one revolute and six cylinder pairs and single loop R-C-R-R-P-R, R-C-R-R-R-R six-link mechanisms are examined to obtain closed form displacement relationships between independent and dependent displacement parameters. Displacement analyses are performed to illustrate the use of these displacement relationships.

scholarly journals A Transmissibility for Single-Loop Spatial Mechanisms

1978 ◽  
Vol 44 (383) ◽  
pp. 2497-2504
Author(s):  
Hiroshi SHIMOJIMA ◽  
Kiyoshi OGAWA ◽  
Toru KAWANO
Keyword(s):  
Single Loop ◽  
Spatial Mechanisms

Kinematics of a Novel Single-Loop Under-Actuated Wrist

2012 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Path Planning ◽  
Closed Form ◽  
Nonholonomic Constraint ◽  
Three Dimensional ◽  
Single Loop ◽  
Closed Form Solutions ◽  
Position Analysis ◽  
Tracking Tasks ◽  
Planning Algorithm ◽  
Path Planning Algorithm

A novel type of parallel wrist (PW) is proposed which, differently from previously presented PWs, features a single-loop architecture and only one nonholonomic constraint. Due to the presence of a nonholonomic constraint, the proposed PW type is under-actuated, that is, it is able to control the platform orientation in a three-dimensional workspace by employing only two actuated pairs, one prismatic (P) and the other revolute (R); and it cannot perform tracking tasks. Position analysis and path planning of this novel PW are studied. In particular, all the relevant position analysis problems are solved in closed form, and, based on these closed-form solutions, a path-planning algorithm is built.

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.

Kinematic Analysis of Spatial Mechanisms Via Successive Screw Displacements

1975 ◽  
Vol 97 (2) ◽  
pp. 739-747 ◽  
Author(s):  
Dilip Kohli ◽  
A. H. Soni
Keyword(s):  
Closed Form ◽  
Kinematic Analysis ◽  
Closed Loop ◽  
Displacement Velocity ◽  
Spatial Mechanism ◽  
Spatial Mechanisms ◽  
Straight Line ◽  
Unified Method

A new, unified method is proposed and demonstrated to conduct kinematic analysis of spatial mechanisms involving revolute, cylindrical, prismatic, helical and spherical pairs. The paper derives the equations for the successive screw displacements, and the equations for pair constraints. Using these equations, closed-form relationships for displacement, velocity and acceleration of single or multi-loop spatial mechanisms are obtained by (1) breaking the mechanism at a critical joint (2) unfolding the mechanism along a straight line (3) providing successive screw displacement at each joint and (4) reassembling the mechanism to form a closed loop. The application of this newly developed approach is demonstrated by considering an example of a two-loop spatial mechanism with revolute, cylindrical and spherical pairs.

scholarly journals A Transmissibility for Single-Loop Spatial Mechanisms

1979 ◽  
Vol 22 (165) ◽  
pp. 405-411 ◽  
Author(s):  
Hiroshi SHIMOJIMA ◽  
Kiyoshi OGAWA ◽  
Toru KAWANO
Keyword(s):  
Single Loop ◽  
Spatial Mechanisms

ON THE SIMPLE STATIONARY CONFIGURATIONS OF SINGLE-LOOP SPATIAL N-REVOLUTE OVERCONSTRAINED LINKAGES

1996 ◽  
Vol 20 (1) ◽  
pp. 17-39 ◽  
Author(s):  
Chung-Ching Lee
Keyword(s):  
Computer Graphics ◽  
Differential Equations ◽  
Range Of Motion ◽  
Closed Form ◽  
Single Loop ◽  
Closed Form Solutions ◽  
Systematic Formulation ◽  
Overconstrained Linkages

Based on the derived matrix and its differential equations, a systematic formulation is presented to either identify the simple stationary configurations of movable spatial 4R, 5R and 6R overconstrained linkages or prove none of them occurs at all. Some examples are given to confirm the correctness and validity of the derived mathematical criterion. In addition, the closed-form solutions of linkage joint variables are well-established and with the help of computer graphics, geometrical meanings of linkage configurations are described. This approach can be used to provide a foundation for understanding the range of motion in overconstrained linkage application.

Automatic Closed-Form Kinematics-Solutions for Recursive Single-Loop Chains

1992 ◽  
Author(s):  
Andrés Kecskeméthy ◽  
Manfred Hiller
Keyword(s):  
Closed Form ◽  
Isotropy Group ◽  
Projection Operators ◽  
Closure Condition ◽  
Single Loop ◽  
Closed Form Solutions ◽  
Point Line ◽  
Geometric Elements ◽  
Scalar Equations

Abstract Described in this paper is a simplified method for the automatic detection and formulation of closed-form solutions for a special class of recursively solvable single-loop mechanisms. The objective is to generate a cascade of scalar equations from the closure condition of the loop, each containing exactly one unknown more than the predecessors, and each being maximally second-order in this unknown. In the proposed method this problem is reduced to the repeated determination of two subchains which are members of the isotropy group of either of the geometric elements point, line and plane and containing as much current unknowns as possible. The scalar equations then arise from unique projection operators applied to unique equation partitionings of the closure condition. This yields a general but easy-to-implement algorithm. The concepts are illustrated with some examples processed with an implementation in Mathematica based on the geometric elements point and plane.

Closed Form Solutions for Connectivity and Connectivity of Motion in Mechanisms

2000 ◽  
Author(s):  
D. Kohli ◽  
N. Razmara ◽  
A. K. Dhingra
Keyword(s):  
Graph Theory ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Open Chain ◽  
Closed Loops ◽  
Closed Form Solutions ◽  
Spatial Mechanisms ◽  
Special Arrangement

Abstract This paper presents a closed form solution for determining connectivity between any two links in mechanism. The formulation is based on graph theory and its modification. The proposed approach could be applied to both planar and spatial mechanisms including combined planar-spatial mechanisms. Further, the mechanism may have multiple closed loops and/or open-chain substructures. A new concept of Connectivity of Motion has been introduced to determine the connectivity between any two links when the mechanism under consideration has special arrangement of adjacent joints such as joints with parallel and/or intersecting axes. Four examples are presented to illustrate connectivity calculations in spatial mechanisms.

Singularity Analysis of a Single-Loop Underactuated Wrist

2013 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Path Planning ◽  
Closed Form ◽  
Nonholonomic Constraint ◽  
Singularity Analysis ◽  
The Novel ◽  
Single Loop ◽  
Position Analysis ◽  
Singular Configurations ◽  
Geometric Conditions

In a previous paper, this author proposed a novel type of underactuated parallel wrist (PW) with a single-loop architecture containing only one nonholonomic constraint. Moreover, he addressed its position analysis and path planning and showed that closed-form formulas can be used to solve all the finite-kinematics problems involved in the path planning of the novel PW. Here, the instantaneous kinematics and the singularity analysis of this PW are addressed. In particular, both the analytic and geometric conditions which identify the singular configurations are presented together with their static interpretation. The presented results are relevant for designing this type of PWs.

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