A Generalized Transmission Index for Spatial Linkages

2005 ◽  
Author(s):  
Chao Chen ◽  
Jorge Angeles
Keyword(s):  
Single Loop ◽  
Spatial Mechanisms ◽  
Transmission Index ◽  
Spatial Linkages

This paper proposes a generalized transmission index for spatial mechanisms, based on the transmission index introduced by Sutherland and Roth. This index is more general and welldefined in all the cases; it matches the virtual coefficient between the transmission wrench screw and the output twist screw exactly. A method is developed to compute the transmission wrench screw in spatial single-loop linkages. We illustrate the application of this index in a RSCR linkage.

A Transmission Index for Spatial Mechanisms

1973 ◽  
Vol 95 (2) ◽  
pp. 589-597 ◽  
Author(s):  
G. Sutherland ◽  
B. Roth
Keyword(s):  
Error Characteristics ◽  
General Index ◽  
Spatial Mechanisms ◽  
Transmission Index ◽  
Quality Of Motion ◽  
Spatial Linkages

A general index of the quality of motion transmission for spatial mechanisms is developed using the theory of screws. This index is shown to be related to the mechanical error possible in a linkage. A method for synthesizing spatial linkages with desirable motion transmission and mechanical error characteristics is developed and examples are shown for the RGGR linkage.

Velocity, Acceleration, and Static-Force Analyses of Spatial Linkages

1965 ◽  
Vol 32 (4) ◽  
pp. 903-910 ◽  
Author(s):  
J. Denavit ◽  
R. S. Hartenberg ◽  
R. Razi ◽  
J. J. Uicker
Keyword(s):  
Virtual Work ◽  
Algebraic Method ◽  
Degree Of Freedom ◽  
Static Force ◽  
Virtual Displacement ◽  
Single Loop ◽  
Loop Equation ◽  
The Matrix ◽  
Spatial Linkages

The algebraic method using 4 × 4 matrices is extended to the analysis of velocities, accelerations, and static forces in one-degree-of-freedom, single-loop, spatial linkages consisting of revolute and prismatic pairs, either singly or in combination. The methods are well suited for machine calculations and have been tested on a number of examples, one of which is presented. Velocities and accelerations are obtained by differentiation of the matrix-loop or position equation. Static forces are found by combining the method of virtual work with the matrix-loop equation to relate the virtual displacement of the load to given virtual deformations of the links.

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

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.

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

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

On the Input Joint Rotation Space and Mobility of Linkages

2008 ◽  
Vol 130 (9) ◽  
Author(s):  
Kwun-Lon Ting
Keyword(s):  
Visualization Tool ◽  
Mobility Analysis ◽  
Joint Rotation ◽  
Single Loop ◽  
Spatial Linkages ◽  
One To One ◽  
Spherical Linkages ◽  
Virtual Loop

This paper presents the concept and application of input joint rotation space of linkages and offers updates on the N-bar rotatability laws. A thorough discussion on the joint rotation space of single-loop planar five-bar linkages is first presented. The concept is then extended to spherical linkages and the generalization to N-bar linkages is discussed. It offers a visualization tool for the input joint rotatability and fills up a void in the N-bar rotatability laws regarding the coordination among multiple inputs. It explains the formation of branches and how to establish a one-to-one correspondence between the inputs and the linkage configurations. The applications to multiloop linkages and spatial linkages are highlighted with Stephenson six-bar linkages, geared linkages, and spatial RCRCR mechanisms. These examples exhibit simplicity and benefits of the proposed concept to the mobility analysis of diversified mechanisms. The concept of virtual loop in spatial linkages is proposed and demonstrated with simple RCRCR and Stephenson six-bar mechanisms.

Dynamic Characteristics of Spatial Mechanisms

1969 ◽  
Vol 91 (1) ◽  
pp. 228-233 ◽  
Author(s):  
E. J. Givens ◽  
J. C. Wolford
Keyword(s):  
Linkage Analysis ◽  
Dynamic Characteristics ◽  
Energy Method ◽  
Planar Mechanisms ◽  
Matrix Methods ◽  
Digital Computation ◽  
Spatial Mechanisms ◽  
Spatial Linkages

An energy method given by Quinnfor determining the dynamic characteristics of planar mechanisms under the action of displacement-related forces is extended to spatial linkages. These linkages may, in addition, be subjected to time-related forces or to velocity-related damping forces. Recently developed matrix methods are used in the linkage analysis resulting in a method well suited to digital computation.

FORCE-AND-MOTION-TRANSMISSION EVALUATION IN SPATIAL MECHANISMS

2005 ◽  
Vol 29 (4) ◽  
pp. 527-539
Author(s):  
Chao Chen ◽  
Jorge Angeles
Keyword(s):  
Force Transmission ◽  
Pressure Angle ◽  
Spatial Mechanisms ◽  
Force And Motion ◽  
Transmission Index ◽  
Transmission Quality ◽  
Special Case

We propose a generalized transmission index for spatial mechanisms, based on the virtual coefficient between the transmission wrench screw and the output twist screw. Compared with other indices, ours is well defined in any case and able to evaluate the force transmission quality more precisely. We apply this index to mechanisms with higher pairs and show that the pressure angle is a special case of our index.

A Dual Number Approach to the Kinematic Analysis of Spatial Linkages With Dimensional and Geometric Tolerances

2004 ◽  
Author(s):  
Emanuele Cecchini ◽  
Ettore Pennestri` ◽  
Roberto Stefanelli ◽  
Leonardo Vita
Keyword(s):  
Kinematic Analysis ◽  
Tolerance Analysis ◽  
Rigid Bodies ◽  
Kinematic Modeling ◽  
Spatial Mechanisms ◽  
Analysis And Synthesis ◽  
Spatial Linkages ◽  
Joint Clearances ◽  
First Time ◽  
Cardan Joint

Design robustness is somewhat connected to tolerances. In fact, the lower is the sensitivity of the kinematic function to the deviations of manufacturing process, the higher is the robustness of the design. In this investigation is described a tolerance analysis method based on dual vectors kinematic modeling of spatial linkages and on Monte Carlo simulation of the random variables. In the present analysis the hypothesis of rigid bodies is valid and only kinematic variables are considered in output. The method is applied to a Cardan joint modelled as an RCCC linkage with main dimensions considered as stochastic variables with Gaussian distribution. Dual vectors are well known in kinematic analysis and synthesis of spatial mechanisms. When compared with traditional vectorial methods, dual vectors show an enhanced capability to model misalignments among kinematic pairs axes. Although this is not the first time that dual vectors are used for the kinematic and dynamic analysis of spatial mechanisms with manufacturing errors, the present use of dual vectors to model joint clearances seems somewhat novel.

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