Synthesis of Planar, Shape-Changing Rigid Body Mechanisms Approximating Closed Curves

2007 ◽  
Author(s):  
Justin A. Persinger ◽  
James P. Schmiedeler ◽  
Andrew P. Murray
Keyword(s):  
Numerical Optimization ◽  
Shape Change ◽  
Closed Curves ◽  
Single Degree Of Freedom ◽  
Revolute Joints ◽  
Planar Shape ◽  
A Chain ◽  
Planar Linkages ◽  
Arc Lengths ◽  
Synthesis Approach

This paper presents a procedure to synthesize planar linkages, composed of rigid links and revolute joints, that are capable of approximating a shape change defined by a set of closed curves possessing similar arc lengths. The synthesis approach is more rigorous and more broadly applicable to dramatic changes between larger numbers of shapes than existing techniques that employ graphical methods. Link geometry is determined through an existing procedure, and those links are then joined together in a chain using numerical optimization to minimize the error in approximating the shape change. Binary links are added to this chain via a search of the design space such that actuated links can be driven monotonically to exact the shape change. The focus is single-degree-of-freedom (DOF) mechanisms that approximate closed curves, but the methodology is similarly applicable to generating mechanisms approximating sets of open curves and multi-DOF systems. The procedure is applied to synthesize an example mechanism that changes between circular, elliptical, and teardrop shapes as inspired by an aerodynamic flow field modification application.

Synthesis of Planar Rigid-Body Mechanisms Approximating Shape Changes Defined by Closed Curves

2009 ◽  
Vol 131 (7) ◽  
Author(s):  
Justin A. Persinger ◽  
James P. Schmiedeler ◽  
Andrew P. Murray
Keyword(s):  
Numerical Optimization ◽  
Shape Change ◽  
Closed Curves ◽  
Single Degree Of Freedom ◽  
Revolute Joints ◽  
A Chain ◽  
Planar Linkages ◽  
Arc Lengths ◽  
Synthesis Approach ◽  
Shape Changes

This paper presents a procedure to synthesize planar linkages, composed of rigid links and revolute joints, that are capable of approximating a shape change defined by a set of closed curves possessing similar arc lengths. The synthesis approach is more rigorous and more broadly applicable to dramatic changes between larger numbers of shapes than existing techniques that employ graphical methods. It specifically addresses the challenges of approximating closed curves, but the methodology is equally applicable to open curves. Link geometry is determined through an existing procedure, and those links are then joined together in a chain using numerical optimization to minimize the error in approximating the shape change. Binary links are added to this chain via a search of the design space, forming a single-degree-of-freedom mechanism in which an actuated link can be driven monotonically to exact the shape change. The procedure is applied to synthesize an example mechanism that changes between circular, elliptical, and teardrop shapes as inspired by an aerodynamic flow field modification application.

Synthesis of Planar, Shape-Changing Rigid-Body Mechanisms

2006 ◽  
Author(s):  
Brian M. Korte ◽  
Andrew P. Murray ◽  
James P. Schmiedeler
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Shape Change ◽  
Piecewise Linear ◽  
Single Chain ◽  
Open Chain ◽  
Revolute Joints ◽  
Planar Shape ◽  
Rigid Body Displacement ◽  
Planar Linkages

This paper presents a procedure to synthesize planar linkages, composed of rigid links and revolute joints, capable of approximating a shape change defined by a set of curves. These “morphing curves” differ from each other by a combination of rigid-body displacement and shape change. Rigid link geometry is determined through analysis of piecewise linear curves to achieve shape-change approximation, and increasing the number of links improves the approximation. A mechanism is determined through connecting the rigid links into a single chain and adding dyads to eliminate degrees of freedom. The procedure is applied to two open-chain examples.

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.

Kinematic Synthesis of Planar, Shape-Changing Rigid-Body Mechanisms

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Andrew P. Murray ◽  
James P. Schmiedeler ◽  
Brian M. Korte
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Shape Change ◽  
Piecewise Linear ◽  
Single Chain ◽  
Planar Mechanisms ◽  
Revolute Joints ◽  
Planar Shape ◽  
Rigid Body Displacement ◽  
Shape Changes

This paper presents a kinematic procedure to synthesize planar mechanisms, composed of rigid links and revolute joints, capable of approximating a shape change defined by a set of curves. These “morphing curves”, referred to as design profiles, differ from each other by a combination of rigid-body displacement and shape change. Design profiles are converted to piecewise linear curves, referred to as target profiles, that can be readily manipulated. In the segmentation phase, the geometry of rigid links that approximate the shapes of corresponding segments from each target profile is determined. In the mechanization phase, these rigid links are joined together at their end points with revolute joints to form a single chain. Dyads are then added to reduce the number of degrees of freedom (DOF’s) to any desired value, typically 1. The approach can be applied to any number of design profiles that can be approximated with any number of rigid links, which can then be used to construct a mechanism with any number of DOF’s. Naturally, greater difficulty is encountered for larger numbers of design profiles and/or links and for more dramatic changes in shape. The procedure is demonstrated with examples of single-DOF mechanisms approximating shape changes between two and three design profiles.

scholarly journals Kinematic Synthesis of Planar, Shape-Changing Rigid Body Mechanisms for Design Profiles With Significant Differences in Arc Length

2011 ◽  
Author(s):  
Shamsul A. Shamsudin ◽  
Andrew P. Murray ◽  
David H. Myszka ◽  
James P. Schmiedeler
Keyword(s):  
Rigid Body ◽  
Shape Change ◽  
Rigid Bodies ◽  
Arc Length ◽  
Shape Variation ◽  
Planar Mechanisms ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Plane Shape ◽  
A Chain

This paper presents a kinematic procedure to synthesize planar mechanisms capable of approximating a shape change defined by a general set of curves. These “morphing curves”, referred to as design profiles, differ from each other by a combination of displacement in the plane, shape variation, and notable differences in arc length. Where previous rigid-body shape-change work focused on mechanisms composed of rigid links and revolute joints to approximate curves of roughly equal arc length, this work introduces prismatic joints into the mechanisms in order to produce the different desired arc lengths. A method is presented to inspect and compare the profiles so that the regions are best suited for prismatic joints can be identified. The result of this methodology is the creation of a chain of rigid bodies connected by revolute and prismatic joints that can approximate a set of design profiles.

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.

Synthesizing Mechanical Chains for Morphing Between Spatial Curves

2020 ◽  
Vol 12 (2) ◽  
Author(s):  
Yucheng Li ◽  
Andrew P. Murray ◽  
David H. Myszka
Keyword(s):  
Shape Change ◽  
Two Dimensions ◽  
Revolute Joints ◽  
Spatial Features ◽  
Morphometric Analyses ◽  
Helical Segment ◽  
A Chain ◽  
Curvature And Torsion ◽  
Synthesis Methodology ◽  
Spatial Curves

Abstract This paper extends the kinematic synthesis methodology for designing a chain of bodies to match a set of arbitrary curves to the spatial case. The methodology initiates with an arbitrary set of spatial curves, and concludes with a set of bodies defined by their spatial features. The bodies synthesized can be one of three types: a rigid segment, a helical segment with constant curvature and torsion but varying length, and a growth segment that maintains its geometry but may be scaled to become larger or smaller. To realize mechanical chains for mechanisms that achieve spatial shape change, only rigid and helical segments are used. After designing the segments, they may be aligned with the original spatial curves with their ends connected via an optimization. For two curves, these connections may be made with revolute joints to obtain high accuracy. For three or more curves, spherical joint connections allow for best accuracy. To compare curves as is useful in morphometry, all three segment types may be employed. In this case, an accurate description of the changes between curves is important, and optimizing to connect the segments is not needed. The procedure for redefining the curves in a way that the techniques in this paper may be applied, as well as the methodologies for synthesizing the three segment types are presented. Examples include a continuum robot problem and the morphometric analyses of cochlear curves and the lambdoidal suture located on a human skull. This work extends the established planar techniques for synthesizing mechanisms and addressing morphometric issues that are motivated with curves in two-dimensions.

Kinematic Synthesis of Planar, Shape-Changing Rigid-Body Mechanisms With Prismatic Joints

2011 ◽  
Author(s):  
Kai Zhao ◽  
James P. Schmiedeler ◽  
Andrew P. Murray
Keyword(s):  
Rigid Body ◽  
Shape Change ◽  
Weighted Least Squares ◽  
Solution Space ◽  
Building Blocks ◽  
Optimization Method ◽  
Basic Block ◽  
Closed Curves ◽  
Revolute Joints ◽  
Prismatic Joints

This paper presents a procedure to synthesize planar rigid-body mechanisms, containing both prismatic and revolute joints, capable of approximating a shape change defined by a set of morphing curves in different positions. With the introduction of prismatic joints, the existing mechanization process needs to be revisited via a building-block approach. The basic block is the Assur group of class II, and the auxiliary block is a fourbar mechanism, crank slider or binary link. To approximate shape changes defined by both open and closed curves, a single degree-of-freedom (DOF) mechanism is generated by assembling these building blocks. In the case of a large number of morphing curves, a weighted least squares approach is applied to determine center point locations for revolute joints and sliding paths for prismatic joints in individual building blocks. Then, the building blocks are located in an assembly position to regenerate the morphing chain using a numerical optimization method. Because of the additional constraints associated with prismatic joints compared to revolute joints, the size of the solution space is reduced, so random searches of the design space to find solution mechanisms are ineffective. A genetic algorithm is employed here instead to find a group of viable designs within reasonable computational limits. The procedure is demonstrated with synthesis examples of two 1-DOF mechanisms, one approximating five open-curve profiles and the other four closed-curve profiles.

A Method for Detection of Distinct Mechanisms of a Planar Kinematic Chain

1988 ◽  
Vol 12 (1) ◽  
pp. 15-20 ◽  
Author(s):  
L.K. Patel ◽  
A.C. Rao
Keyword(s):  
Efficient Method ◽  
Numerical Scheme ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
A Chain

This paper presents a computationally simple and efficient method for identification of distinct mechanisms of a planar kinematic chain having a single degree of freedom. It is proposed that velocity diagrams for all the inversions of a chain be drawn and the possible isomorphism among these velocity diagrams be detected. From the velocity diagram, a motion transfer point matrix can be prepared resulting in the development of a numerical scheme to be associated with a mechanism. Identical schemes lead to detection of isomorphism between mechanisms. The main advantage of this method is that, apart form detecteing isomorphism, it indicates which of the inversions is better kinematically e.g. higher the total number of vectors, better is the mechanism.

Design and Analysis of Reduced Degree of Freedom Modular Snake Robot

2017 ◽  
Author(s):  
Peter Racioppo ◽  
Wael Saab ◽  
Pinhas Ben-Tzvi
Keyword(s):  
Three Dimensional ◽  
Cross Sectional ◽  
Design Synthesis ◽  
Snake Robot ◽  
Routing Schemes ◽  
Revolute Joints ◽  
Modular Units ◽  
A Chain ◽  
The Moment ◽  
And Control

This paper presents the design and analysis of an underactuated, cable driven mechanism for use in a modular robotic snake. The proposed mechanism is composed of a chain of rigid links that rotate on parallel revolute joints and are actuated by antagonistic cable pairs and a multi-radius pulley. This design aims to minimize the cross sectional area of cable actuated robotic snakes and eliminate undesirable nonlinearities in cable displacements. A distinctive feature of this underactuated mechanism is that it allows planar serpentine locomotion to be accomplished with only two modular units, improving the snake’s ability to conform to desired curvature profiles and minimizing the control complexity involved in snake locomotion. First, the detailed mechanism and cable routing scheme are presented, after which the kinematics and dynamics of the system are derived and a comparative analysis of cable routing schemes is performed, to assist with design synthesis and control. The moment of inertia of the mechanism is modeled, for future use in the implementation of three-dimensional modes of snake motion. Finally, a planar locomotion strategy for snake robots is devised, demonstrated in simulation, and compared with previous studies.

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