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.

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.

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.

scholarly journals Miura-ori, Basics for Designing its Folding Machines

2019 ◽  
Vol 2 ◽  
pp. 1-5
Author(s):  
Koryo Miura
Keyword(s):  
Basic Concept ◽  
High Speed ◽  
Geometric Property ◽  
Unique Property ◽  
Degree Of Freedom ◽  
Design Parameters ◽  
Geometric Properties ◽  
Single Degree Of Freedom ◽  
Single Degree

<p><strong>Abstract.</strong> The unique property of the Miura-ori map is due to the geometric property of “the single degree of freedom”. With this, one can open a map with a single pull motion. However, due to this property, the high-speed folding machine is difficult to realized. In this presentation, author investigates the natural geometric properties of Miura-ori in detail and proposes a basic concept for designing its folding machine. Though, the result does not provide a draft of a folding machine, the basics for the design parameters is beneficial for future works.</p>

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.

Three-Position Synthesis of Origami-Evolved, Spherically Constrained Spatial Revolute–Revolute Chains

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Kassim Abdul-Sater ◽  
Manuel M. Winkler ◽  
Franz Irlinger ◽  
Tim C. Lueth
Keyword(s):  
Building Blocks ◽  
Design Parameters ◽  
Specific Task ◽  
Spherical Design ◽  
Single Degree Of Freedom ◽  
End Effector ◽  
Single Degree ◽  
Folding Pattern ◽  
Position Synthesis ◽  
Space Requirements

This paper presents a finite position synthesis (f.p.s.) procedure of a spatial single-degree-of-freedom linkage that we call origami-evolved, spherically constrained spatial revolute–revolute (RR) chain here. This terminology is chosen because the linkage may be found from the mechanism equivalent of an origami folding pattern, namely, known as the Miura-ori folding. As shown in an earlier work, the linkage under consideration has naturally given slim shape and essentially represents two specifically coupled spherical four-bar linkages, whose links may be identified with spherical and spatial RR chains. This provides a way to apply the well-developed f.p.s. theory of these linkage building blocks in order to design the origami-evolved linkage for a specific task. The result is a spherically constrained spatial RR chain, whose end effector may reach three finitely separated task positions. Due to an underspecified spherical design problem, the procedure provides several free design parameters. These can be varied in order to match further given requirements of the task. This is shown in a design example with particularly challenging space requirements, which can be fulfilled due to the naturally given slim shape.

A Finite-Element-Based Method to Determine the Spatial Stiffness Properties of a Notch Hinge

1998 ◽  
Vol 123 (1) ◽  
pp. 141-147 ◽  
Author(s):  
Shilong Zhang ◽  
Ernest D. Fasse
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Joint Stiffness ◽  
Degree Of Freedom ◽  
Design Parameters ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Stiffness Properties ◽  
Six Degree Of Freedom ◽  
Flexural Hinges

Notch hinges are flexural hinges used to make complex, precise mechanisms. They are typically modeled as single degree-of-freedom hinges with an associated joint stiffness. This is not adequate for all purposes. This paper computes the six degree-of-freedom stiffness properties of notch hinges using finite element methods. The results are parameterized in terms of meaningful design parameters.

Design of a Cam-Actuated Robotic Leg

2014 ◽  
Author(s):  
Diane L. Peters ◽  
Steven Chen
Keyword(s):  
Optimization Problem ◽  
Angular Displacement ◽  
Design Parameters ◽  
Single Degree Of Freedom ◽  
Advantages And Disadvantages ◽  
Single Degree ◽  
Error Metric ◽  
Robotic Leg ◽  
Foot Position ◽  
Leg Design

This paper presents a concept for a single-degree-of-freedom robotic leg, where the lower and upper leg are each controlled by a cam. The two cams are mounted on a common shaft, and are rotating at the same speed. The relevant equations for the mechanism’s kinematics are first developed, to express the position of the foot in terms of the cam’s angular displacement and various design parameters such as link lengths. Next, the design problem is formulated as an optimization, where the objective is to minimize an error metric that compares the foot position to the desired trajectory of the foot. The constraints in the optimization problem include important parameters such as the pressure angle of the cams, as well as a set of constraints to ensure that the leg will fit on an appropriately sized legged robot. Finally, the results are discussed, with a focus on what the advantages and disadvantages of this leg design might be as compared to other types of robotic leg designs.

Computer Analysis of the Dynamic Contact Behavior and Tracking Characteristics of a Single-Degree-of-Freedom Slider Model for a Contact Recording Head

1995 ◽  
Vol 117 (1) ◽  
pp. 124-129 ◽  
Author(s):  
Kyosuke Ono ◽  
Hiroshi Yamamura ◽  
Takaaki Mizokoshi
Keyword(s):  
Contact Stiffness ◽  
Time History ◽  
Dynamic Contact ◽  
Disk Surface ◽  
Degree Of Freedom ◽  
Design Parameters ◽  
Single Degree Of Freedom ◽  
Contact Behavior ◽  
Single Degree ◽  
Contact Slider

This paper presents a new theoretical approach to the dynamic contact behavior and tracking characteristics of a contact slider that is one of the candidates of head design for future high density magnetic recording disk storages. A slider and its suspension are modeled as a single-degree-of-freedom vibration system. The disk surface is assumed to have a harmonic wavy roughness with linear contact stiffness and damping. From the computer simulation of the time history of the slider motion after dropping from the initial height of 10 nm, it is found that the contact vibration of the slider can attenuate and finally track on the wavy disk surface in a low waviness frequency range. As the waviness frequency increases, however, the slider cannot stay on the disk surface and comes to exhibit a variety of contact vibrations, such as sub- and super-harmonic resonance responses and finally comes to exhibit non-periodic vibration. It is also found that, among design parameters, the slider load to mass ratio and contact damping can greatly increase the surface waviness frequency and amplitude for which the stable tracking of a contact slider is possible.

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