Mechanism Branches, Turning Curves, and Critical Points

2012 ◽  
Author(s):  
David H. Myszka ◽  
Andrew P. Murray ◽  
Charles W. Wampler
Keyword(s):  
Critical Points ◽  
Design Parameter ◽  
Turning Point ◽  
Closed Loop ◽  
Turning Points ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Point Curve ◽  
General Method ◽  
Number Of Branches

This paper considers single-degree-of-freedom, closed-loop linkages with a designated input angle and one design parameter. For a fixed value of the design parameter, a linkage has turning points (dead-input singularities), which break the motion curve into branches such that the motion along each branch can be driven monotonically from the input. As the design parameter changes, the number of branches and their connections, in short the topology of the motion curve, may change at certain critical points. As the design parameter changes, the turning points sweep out a curve we call the “turning curve,” and the critical points are the singularities in this curve with respect to the design parameter. The critical points have succinct geometric interpretations as transition linkages. We present a general method to compute the turning curve and its critical points. As an example, the method is used on a Stephenson II linkage. Additionally, the Stephenson III linkage is revisited where the input angle is able to rotate more than one revolution between singularities. This characteristic is associated with cusps on the turning point curve.

Computing the Branches, Singularity Trace, and Critical Points of Single Degree-of-Freedom, Closed-Loop Linkages

2013 ◽  
Vol 6 (1) ◽  
Author(s):  
David H. Myszka ◽  
Andrew P. Murray ◽  
Charles W. Wampler
Keyword(s):  
Critical Points ◽  
Design Parameter ◽  
Closed Loop ◽  
Turning Points ◽  
Critical Curve ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
General Method ◽  
Number Of Branches

This paper considers single degree-of-freedom (DOF), closed-loop linkages with a designated input angle and one design parameter. For a fixed value of the design parameter, a linkage has input singularities, that is, turning points with respect to the input angle, which break the motion curve into branches. Motion of the linkage along each branch can be driven monotonically from the input. As the design parameter changes, the number of branches and their connections, in short the topology of the motion curve, may change at certain critical points. Allowing the design parameter to vary, the singularities form a curve called the critical curve, whose projection is the singularity trace. Many critical points are the singularities of the critical curve with respect to the design parameter. The critical points have succinct geometric interpretations as transition linkages. This paper presents a general method to compute the singularity trace and its critical points. As an example, the method is used on a Stephenson III linkage, and a range of the design parameter is found where the input angle is able to rotate more than one revolution between singularities. This characteristic is associated with critical points that appear as cusps on the singularity trace.

scholarly journals Using the Singularity Trace to Understand Linkage Motion Characteristics

2013 ◽  
Author(s):  
Lin Li ◽  
David H. Myszka ◽  
Andrew P. Murray ◽  
Charles W. Wampler
Keyword(s):  
Critical Points ◽  
Design Parameter ◽  
Closed Loop ◽  
Design Parameters ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Net Zero ◽  
Motion Characteristics ◽  
Number Of Branches ◽  
Activation Sequence

This paper provides examples of a method used to analyze the motion characteristics of single-degree-of-freedom, closed-loop linkages under study a designated input angle and one or two design parameters. The method involves the construction of a singularity trace, which is a plot that reveals changes in the number of geometric inversions, singularities, and changes in the number of branches as a design parameter is varied. This paper applies the method to Watt II, Stephenson III and double butterfly linkages. For the latter two linkages, instances where the input angle is able to rotate more than one revolution between singularities have been identified. This characteristic demonstrates a net-zero, singularity free, activation sequence that places the mechanism into a different geometric inversion. Additional observations from the examples are given. Instances are shown where the singularity trace for the Watt II linkage includes multiple coincident projections of the singularity curve. Cases are shown where subtle changes to two design parameters of a Stephenson III linkage drastically alters the motion. Additionally, isolated critical points are found to exist for the double butterfly, where the linkage becomes a structure and looses the freedom to move.

Singularity Traces of Single Degree-of-Freedom Planar Linkages That Include Prismatic and Revolute Joints

2016 ◽  
Vol 8 (5) ◽  
Author(s):  
Saleh M. Almestiri ◽  
Andrew P. Murray ◽  
David H. Myszka ◽  
Charles W. Wampler
Keyword(s):  
Design Parameter ◽  
Closed Loop ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Motion Characteristics ◽  
Planar Linkages ◽  
General Method

This paper extends the general method to construct a singularity trace for single degree-of-freedom (DOF), closed-loop linkages to include prismatic along with revolute joints. The singularity trace has been introduced in the literature as a plot that reveals the gross motion characteristics of a linkage relative to a designated input joint and a design parameter. The motion characteristics identified on the plot include a number of possible geometric inversions (GIs), circuits, and singularities at any given value for the input link and the design parameter. An inverted slider–crank and an Assur IV/3 linkage are utilized to illustrate the adaptation of the general method to include prismatic joints.

Handwriting: A Perceptual-Motor Disturbance in Children with Myelomeningocele

1990 ◽  
Vol 10 (1) ◽  
pp. 12-26 ◽  
Author(s):  
Jenny Ziviani ◽  
Alan Hayes ◽  
David Chant
Keyword(s):  
Skill Acquisition ◽  
Closed Loop ◽  
Statistical Significance ◽  
Regression Analyses ◽  
Single Degree Of Freedom ◽  
Motor Disturbance ◽  
Motor Skill Acquisition ◽  
Single Degree ◽  
Scholastic Aptitude ◽  
Effect Of Age

An explanation for the handwriting difficulties experienced by children with spina bifida myelomeningocele was sought within the framework of a closed-loop theory of motor skill acquisition. The handwriting performance of 34 children (16 boys and 18 girls) aged 6.16 to 13.42 years was detailed with available norms. Regression analyses were then performed for the five handwriting components of speed, alignment, letter formation, spacing, and size. The regressions for speed, alignment, and letter formation reached statistical significance. For speed, age provided the greatest explanation of performance (R2 = .62, p = .008). Alignment was explained substantially by age, handedness, scholastic aptitude, and kinesthesia (R2 = .55, p = .03). Letter formation was determined primarily by age and kinesthesia (R2 .71, p = .001,). The overall regression was not significant for spacing (R2 = .39, p = .30), or size (R2 = .35, p = .43), although a significant single degree of freedom was detected for the effect of age. These findings are discussed in terms of skill acquisition theory.

A Finite Element Approach to Pad Flexibility Effects in Tilt Pad Journal Bearings: Part I—Single Pad Analysis

1990 ◽  
Vol 112 (2) ◽  
pp. 169-176 ◽  
Author(s):  
L. L. Earles ◽  
A. B. Palazzolo ◽  
R. W. Armentrout
Keyword(s):  
Finite Element ◽  
Current Method ◽  
Journal Bearings ◽  
Radius Of Curvature ◽  
Approximate Methods ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Tilting Pad ◽  
Element Approach ◽  
General Method

A general method of incorporating pad flexibility effects into tilting pad isothermal bearing analysis is developed. The pad assembly approach is extended using 2-dimensional finite elements to determine pad deformations of a single pad. The pad deformations are represented by a single degree of freedom, the change in the pad radius of curvature, thus the current method is an approximate approach. The equations to calculate frequency reduced coefficients for a single pad are presented. Synchronously reduced coefficients for a single pad are in agreement with previous curved beam approximate methods and a more rigorous iterative approach. The finite element pad model provides more versatility in modeling nonuniform pad dimensions and the skewed boundary conditions which occur at the spherical pivot-pad socket interfaces.

Deployable Prismatic Structures With Rigid Origami Patterns

2016 ◽  
Vol 8 (3) ◽  
Author(s):  
Sicong Liu ◽  
Weilin Lv ◽  
Yan Chen ◽  
Guoxing Lu
Keyword(s):  
Closed Loop ◽  
Design Method ◽  
Kinematic Model ◽  
Deployable Structures ◽  
Engineering Applications ◽  
Single Degree Of Freedom ◽  
General Design ◽  
Plane Symmetric ◽  
Single Degree ◽  
Spherical Linkages

Rigid origami inspires new design technology in deployable structures with large deployable ratio due to the property of flat foldability. In this paper, we present a general kinematic model of rigid origami pattern and obtain a family of deployable prismatic structures. Basically, a four-crease vertex rigid origami pattern can be presented as a spherical 4R linkage, and the multivertex patterns are the assemblies of spherical linkages. Thus, this prismatic origami structure is modeled as a closed loop of spherical 4R linkages, which includes all the possible prismatic deployable structures consisting of quadrilateral facets and four-crease vertices. By solving the compatibility of the kinematic model, a new group of 2n-sided deployable prismatic structures with plane symmetric intersections is derived with multilayer, straight and curvy variations. The general design method for the 2n-sided multilayer deployable prismatic structures is proposed. All the deployable structures constructed with this method have single degree-of-freedom (DOF), can be deployed and folded without stretching or twisting the facets, and have the compactly flat-folded configuration, which makes it to have great potential in engineering applications.

The Case for a General Method of Kinematic Analysis of Plane Mechanisms Based on Equations of Constraint

1995 ◽  
Vol 209 (5) ◽  
pp. 337-343 ◽  
Author(s):  
A A Fogarasy ◽  
M R Smith
Keyword(s):  
Kinematic Analysis ◽  
Degree Of Freedom ◽  
Adequate Description ◽  
Single Degree Of Freedom ◽  
Constraint Equations ◽  
Single Degree ◽  
Motion Characteristics ◽  
Clear Line ◽  
Selection Of ◽  
General Method

All but the simplest of single degree of freedom mechanisms have a relatively large number of component parts. To analyse the motion of such systems, therefore, one parameter is rarely sufficient. For an adequate description of the motion characteristics of all components, a number of additional coordinates are needed. This paper introduces a clear and logical notation which facilitates the setting up of the required number of constraint equations by simple inspection of clear line diagrams of the mechanism to be analysed. These constraint equations are eminently suitable for the calculation of velocities and accelerations by direct differentiation. The resulting equations are linear in the velocities and accelerations of all component parts. A method based on this approach is presented and applied to a selection of widely different examples.

scholarly journals Research on a ø6m TBM Steel Arch Splicing Manipulator

2021 ◽  
Author(s):  
Yuanfu He ◽  
Yimin Xia ◽  
Zhen Xu ◽  
Jie Yao ◽  
Bo Ning ◽  
...  
Keyword(s):  
Large Volume ◽  
Closed Loop ◽  
Design Method ◽  
Dynamic Performance ◽  
Structural Stiffness ◽  
Input Constraints ◽  
Positioning Accuracy ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Performance Indexes

Abstract As a challenging task, the robotic splicing of steel arch is required to realize the grasping and docking of steel arches in a limited space. The steel arches often have a mass of over 200kg and a length of over 4m. Due to the large volume and mass of steel arches and the high requirements for the positioning accuracy of splicing, it is difficult for the general manipulator to meet its flexibility and stiffness requirements. The single-degree-of-freedom(DOF) closed-loop mechanism has a simple and reliable structure. Adding it into the manipulator can effectively improve the dynamic performance and increase the structural stiffness. In this paper, a solution model of a single-DOF closed-loop planar mechanism is presented, and alternative kinematic pairs of the mechanism with different input constraints and output requirements are derived. Based on this model, a design method of steel arch splicing manipulator with single-DOF closed-loop grasping structure is proposed. All the optional basic configurations of the manipulator are deduced, and then the optimal configuration is obtained by using the performance indexes. A prototype of the steel arch splicing manipulator is manufactured, and the reliability of the manipulator is proved by experiments.

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