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.

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.

Graphical Methods to Locate the Secondary Instant Centers of Single-Degree-of-Freedom Indeterminate Linkages

2005 ◽  
Vol 127 (2) ◽  
pp. 249-256 ◽  
Author(s):  
David E. Foster ◽  
Gordon R. Pennock
Keyword(s):  
Degree Of Freedom ◽  
Graphical Methods ◽  
Single Degree Of Freedom ◽  
Revolute Joint ◽  
Single Degree ◽  
Revolute Joints ◽  
Straight Line ◽  
Single Link ◽  
Prismatic Joints ◽  
Two Degree Of Freedom

This paper presents graphical techniques to locate the unknown instantaneous centers of zero velocity of planar, single-degree-of-freedom, linkages with kinematic indeterminacy. The approach is to convert a single-degree-of-freedom indeterminate linkage into a two-degree-of-freedom linkage. Two methods are presented to perform this conversion. The first method is to remove a binary link and the second method is to replace a single link with a pair of links connected by a revolute joint. First, the paper shows that a secondary instant center of a two-degree-of-freedom linkage must lie on a unique straight line. Then this property is used to locate a secondary instant center of the single-degree-of-freedom indeterminate linkage at the intersection of two lines. The two lines are obtained from a purely graphical procedure. The graphical techniques presented in this paper are illustrated by three examples of single-degree-of-freedom linkages with kinematic indeterminacy. The examples are a ten-bar linkage with only revolute joints, the single flier eight-bar linkage, and a ten-bar linkage with revolute and prismatic joints.

Graphical Methods to Locate the Secondary Instant Centers of Single-Degree-of-Freedom Indeterminate Linkages

2004 ◽  
Author(s):  
David E. Foster ◽  
Gordon R. Pennock
Keyword(s):  
Degree Of Freedom ◽  
Graphical Methods ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Revolute Joints ◽  
Straight Line ◽  
Single Link ◽  
Prismatic Joints ◽  
Instantaneous Center ◽  
Two Degree Of Freedom

This paper presents graphical techniques to locate the unknown instantaneous centers of zero velocity of planar, single-degree-of-freedom, linkages with kinematic indeterminacy. The approach is to convert a single-degree-of-freedom indeterminate linkage into a two-degree-of-freedom linkage. Two methods are presented to perform this conversion. The first method is to remove a binary link and the second method is to replace a single link with a pair of links connected by a revolute joint. First, the paper shows that a secondary instantaneous center of a two-degree-of-freedom linkage must lie on a unique straight line. Then this property is used to locate a secondary instant center of the single-degree-of-freedom linkage at the intersection of two lines. The two lines are obtained from a purely graphical procedure. The graphical techniques presented in this paper are illustrated by three examples of single-degree-of-freedom linkages with kinematic indeterminacy. The examples are a ten-bar linkage with only revolute joints, the single flier eight-bar linkage, and a ten-bar linkage with revolute and prismatic joints.

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.

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.

Singularity Traces of Planar Linkages That Include Prismatic and Revolute Joints

2015 ◽  
Author(s):  
Saleh M. Almestiri ◽  
David H. Myszka ◽  
Andrew P. Murray ◽  
Charles W. Wampler
Keyword(s):  
Shape Change ◽  
Rigid Bodies ◽  
Closed Curves ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Kinematic Position ◽  
Motion Characteristics ◽  
Forward Kinematic ◽  
Planar Linkages ◽  
General Method

This paper presents a general method to construct a singularity trace for single degree-of-freedom, closed-loop linkages that include prismatic, in addition to, 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 design parameter. Previously, singularity traces were restricted to mechanisms composed of only rigid bodies and revolute joints. The motion characteristics identified on the plot include changes in the number of solutions to the forward kinematic position analysis (geometric inversions), singularities, and changes in the number of branches. To illustrate the adaptation of the general method to include prismatic joints, basic slider-crank and inverted slider-crank linkages are explored. Singularity traces are then constructed for more complex Assur IV/3 linkages containing multiple prismatic joints. These Assur linkages are of interest as they form an architecture that is commonly used for mechanisms capable of approximating a shape change defined by a general set of closed curves.

A New Family of Bricard-Derived Deployable Mechanisms

2016 ◽  
Vol 8 (3) ◽  
Author(s):  
Hailin Huang ◽  
Bing Li ◽  
Jianyang Zhu ◽  
Xiaozhi Qi
Keyword(s):  
Large Volume ◽  
Computer Aided Design ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
New Family ◽  
Revolute Joints ◽  
Computer Aided ◽  
Cad Models ◽  
Aided Design

This paper proposes a new family of single degree of freedom (DOF) deployable mechanisms derived from the threefold-symmetric deployable Bricard mechanism. The mobility and geometry of original threefold-symmetric deployable Bricard mechanism is first described, from the mobility characterstic of this mechanism, we show that three alternate revolute joints can be replaced by a class of single DOF deployable mechanisms without changing the single mobility characteristic of the resultant mechanisms, therefore leading to a new family of Bricard-derived deployable mechanisms. The computer-aided design (CAD) models are used to demonstrate these derived novel mechanisms. All these mechanisms can be used as the basic modules for constructing large volume deployable mechanisms.

Geometric Design of a Bio-Inspired Flapping Wing Mechanism Based on Bennett-Derived 6R Deployable Mechanisms

2014 ◽  
Author(s):  
Huang Hailin ◽  
Li Bing
Keyword(s):  
Flapping Wing ◽  
Geometric Design ◽  
Geometric Parameters ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Flapping Motion ◽  
Single Degree ◽  
Revolute Joints ◽  
Air Vehicle ◽  
Deployable Mechanism

In this paper, we present the concept of designing flapping wing air vehicle by using the deployable mechanisms. A novel deployable 6R mechanism, with the deploying/folding motion of which similar to the flapping motion of the vehicle, is first designed by adding two revolute joints in the adjacent two links of the deployable Bennett linkage. The mobility of this mechanism is analyzed based on a coplanar 2-twist screw system. An intuitive projective approach for the geometric design of the 6R deployable mechanism is proposed by projecting the joint axes on the deployed plane. Then the geometric parameters of the deployable mechanism can be determined. By using another 4R deployable Bennett connector, the two 6R deployable wing mechanisms can be connected together such that the whole flapping wing mechanism has a single degree of freedom (DOF).

An Algorithm for Analytically Calculating the Positions of the Secondary Instant Centers of Indeterminate Linkages

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Analytical Method ◽  
Direct Application ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Planar Mechanism ◽  
Single Degree ◽  
Planar Linkages

In a planar mechanism, the position of the instant centers reveals important pieces of information about its static and kinematic behaviors. Such pieces of information are useful for designing the mechanism. Unfortunately, when the mechanism architecture becomes complex, common methods to locate the instant centers, which are based on the direct application of the Aronold–Kennedy theorem, fail. Indeterminate linkages are single-degree-of-freedom (single-dof) planar linkages where the secondary instant centers cannot be found by direct application of the Aronold–Kennedy theorem. This paper presents an analytical method to locate all the instant centers of any single-dof planar mechanism, which, in particular, succeeds in determining the instant centers of indeterminate linkages. In order to illustrate the proposed method, it will be applied to locate the secondary instant centers of the double butterfly linkage and of the single flier eight-bar linkage.

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