Dwell Motion From Spatial Linkages

1973 ◽  
Vol 95 (2) ◽  
pp. 511-518 ◽  
Author(s):  
A. K. Shrivastava ◽  
K. H. Hunt
Keyword(s):  
Curve Matching ◽  
Single Loop ◽  
Spatial Linkages ◽  
Four Bar Linkage ◽  
Surface Curve

The potential of single-loop spatial linkages to produce an output dwell from a rotating input is broadly surveyed. Then three comparatively simple four-bar linkage arrangements are selected, and studied in detail. The dwell characteristics of all three are viewed via surface-surface or surface-curve “matching” at a spherical pair. Attention is mainly confined to symmetric output-input motions, and the accuracy of dwell is assessed.

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 The Coupler Surface of the RSRS Mechanism

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Nicolas Rojas ◽  
Aaron M. Dollar
Keyword(s):  
Rigid Body ◽  
Interested Reader ◽  
Implicit Equation ◽  
Spatial Mechanism ◽  
Full Equation ◽  
Sextic Curve ◽  
Spatial Linkages ◽  
Robotic Devices ◽  
Four Bar Linkage ◽  
Two Degree Of Freedom

Two degree-of-freedom (2-DOF) closed spatial linkages can be useful in the design of robotic devices for spatial rigid-body guidance or manipulation. One of the simplest linkages of this type, without any passive DOF on its links, is the revolute-spherical-revolute-spherical (RSRS) four-bar spatial linkage. Although the RSRS topology has been used in some robotics applications, the kinematics study of this basic linkage has unexpectedly received little attention in the literature over the years. Counteracting this historical tendency, this work presents the derivation of the general implicit equation of the surface generated by a point on the coupler link of the general RSRS spatial mechanism. Since the derived surface equation expresses the Cartesian coordinates of the coupler point as a function only of known geometric parameters of the linkage, the equation can be useful, for instance, in the process of synthesizing new devices. The steps for generating the coupler surface, which is computed from a distance-based parametrization of the mechanism and is algebraic of order twelve, are detailed and a web link where the interested reader can download the full equation for further study is provided. It is also shown how the celebrated sextic curve of the planar four-bar linkage is obtained from this RSRS dodecic.

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.

Approximate Synthesis of Spatial Linkages

1960 ◽  
Vol 27 (1) ◽  
pp. 201-206 ◽  
Author(s):  
J. Denavit ◽  
R. S. Hartenberg
Keyword(s):  
Helical Motion ◽  
Second Variation ◽  
Variable Pitch ◽  
Approximate Synthesis ◽  
Spatial Linkages ◽  
Four Bar Linkage

Freudenstein’s approximate synthesis of planar four-bar linkages is generalized to spatial linkages, and the conditions under which this generalization is applicable are expressed. Three cases of synthesis of spatial linkages to generate functions of one variable between nonparallel axes are considered in detail: (a) The spherical four-bar linkage; (b) a variation of the four-bar linkage in which two turning pairs are replaced by ball-and-socket joints, a linkage which may be designed to generate arbitrary functions with up to seven accuracy points; and (c) a second variation of the four-bar linkage where three turning pairs are replaced by cylinder pairs, a linkage capable of being designed to generate a variable-pitch helical motion with three accuracy points.

scholarly journals Spatial Straight-Line Linkages by Factorization of Motion Polynomials

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Zijia Li ◽  
Josef Schicho ◽  
Hans-Peter Schröcker
Keyword(s):  
End Effector ◽  
Single Loop ◽  
Revolute Joints ◽  
Straight Line ◽  
Prismatic Joints ◽  
Spatial Linkages ◽  
Line Trajectory ◽  
Straight Line Trajectory

We use the recently introduced factorization of motion polynomials for constructing overconstrained spatial linkages with a straight-line trajectory. Unlike previous examples of such linkages by other authors, they are single-loop linkages and the end-effector motion is not translational. In particular, we obtain a number of linkages with four revolute and two prismatic joints and a remarkable linkage with seven revolute joints one of whose joints performs a Darboux motion.

Joint Rotation Space and Mobility of Linkages

2007 ◽  
Author(s):  
Kwun-Lon Ting
Keyword(s):  
Fundamental Principle ◽  
General Concept ◽  
Joint Rotation ◽  
Single Loop ◽  
Input Domain ◽  
Spatial Linkages ◽  
One To One

The paper presents a general concept regarding the joint rotation space (JRS) of single loop planar and spherical N-bar linkages as well as its significance and applicability in multiple loop and spatial linkages. A JRS refers to the input domain of a linkage. The paper first discusses and classifies the JRS types of single loop five-bar linkages based on the types of the JRS boundary. The concept of sheets and pages of JRS is then introduced as an aid to understand the mobility of linkages. A sheet refers to the JRS of a linkage branch (or circuit). A JRS sheet may have one or more pages and each page refers to an uncertainty singularity free JRS. The concept is then generalized to any single loop planar and spherical N-bar linkages (N ≥ 3). The paper offers geometric insights to the input domain of a linkage and establishes a one-to-one correspondence between the input domain and the linkage configurations. The applications to the mobility identification of complex linkages are discussed and demonstrated with geared five-bar linkages, Stephenson six-bar linkages, as well as spatial RCRCR mechanisms. The paper presents a useful model explaining the fundamental principle regarding the formation of branches and sub-branches in Stephenson six-bar linkages as well as some other multiloop and spatial linkages. The Mobility similarity between multiloop linkages and spatial linkages is also highlighted.

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 New Family of Deployable Mechanisms Derived From Two-Layer and Two-Loop Spatial Linkages With Five Revolute Pair Coupling Chains

2017 ◽  
Vol 9 (6) ◽  
Author(s):  
Wen-ao Cao ◽  
Donghao Yang ◽  
Huafeng Ding
Keyword(s):  
Structural Characteristics ◽  
Degree Of Freedom ◽  
Single Loop ◽  
New Family ◽  
Serial Chain ◽  
Spatial Linkages ◽  
Application Requirements ◽  
Pair Coupling

This paper aims to construct a novel family of deployable mechanisms from a class of two-layer and two-loop spatial linkages, each of which consists of an eight revolute pair (8R) single-loop linkage connected by a 5R serial chain. First, structural characteristics of the class of linkages as deployable units are analyzed and illustrated. Then, the two-layer and two-loop spatial linkages with 5R chains satisfying the structural characteristics are systematically synthesized. Mobile assembly modes between deployable units are established based on degree-of-freedom (DOF) analysis. Finally, a family of single DOF deployable mechanisms is constructed based on the synthesized deployable units and the established assembly modes. The derived deployable mechanisms have the characteristic of the umbrella-like structure, and they have various mesh shapes, which can meet different kinds of application requirements.

Optimization of Spherical Joint Attachment in Spatial Linkages

1988 ◽  
Vol 110 (4) ◽  
pp. 440-445 ◽  
Author(s):  
M. M. Stanisˇic´ ◽  
W. F. Mirusky
Keyword(s):  
Kinematic Analysis ◽  
Optimization Technique ◽  
Spherical Joint ◽  
Spatial Linkages ◽  
Four Bar Linkage

This paper presents the kinematic analysis and optimization technique required for the optimal attachment of a spherical joint (i.e., a ball in a socket) to the ground pivoted link of an RSSR spatial four-bar linkage. The optimization technique is a searching algorithm, which can be applied to the problem of optimal spherical joint attachment in other types of spatial linkages as well. This attachment optimization is necessary if the socket of the joint is to have its maximum ball retention capability. The optimization technique is illustrated by an example.

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