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.

Synthesizing Mechanical Chains for Morphing Between Spatial Curves

2019 ◽  
Author(s):  
Yucheng Li ◽  
Andrew P. Murray ◽  
David H. Myszka
Keyword(s):  
Three Dimensional ◽  
Two Dimensions ◽  
Revolute Joints ◽  
Morphometric Analyses ◽  
Helical Segment ◽  
Varying Length ◽  
A Chain ◽  
Curvature And Torsion ◽  
Synthesis Methodology ◽  
Spatial Curves

Abstract This work investigates the kinematic synthesis methodology for designing a chain of three-dimensional bodies to match a set of arbitrary spatial curves. 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, 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 the 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 chochlear curves and the lambdoidal suture. This work extends the established planar techniques for synthesizing mechanisms and addressing morphometric issues that are motivated with curves in two-dimensions.

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.

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.

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.

Compaction-related deformation in Cambrian olenelloid trilobites and its implications for fossil morphometry

1999 ◽  
Vol 73 (2) ◽  
pp. 355-371 ◽  
Author(s):  
Mark Webster ◽  
Nigel C. Hughes
Keyword(s):  
Lower Cambrian ◽  
Shape Change ◽  
Anterior Lobe ◽  
Interspecific Differences ◽  
Fracture Patterns ◽  
Morphometric Analyses ◽  
Ontogenetic Trajectories ◽  
Metric Distances ◽  
Relative Convexity ◽  
Shape Changes

Morphometric analyses of silicified and nonsilicified (preserved in shale) specimens of the olenelloid trilobites Olenellus (Olenellus) gilberti Meek (in White, 1874) and Nephrolenellus geniculatus Palmer, 1998, from the Lower Cambrian C-Shale Member of the Pioche Formation show that even well-preserved specimens in shales have undergone significant changes in lateral as well as vertical dimensions as a result of compaction. Analyses of cephalic landmarks show that in both species compaction causes posteriordirected collapse of the anterior lobe of the glabella, adaxial deformation of the ocular lobes, and abaxial and anterior splaying of genal regions. These shape changes are explicable in terms of observed exoskeletal fracture patterns. Landmarks show an increase in scatter around their ontogenetic trajectories that is generally proportional to the degree of lateral shift each landmark has undergone. Interspecific differences in compactional response may depend on the relative convexity of the cephalon. Olenellus (Olenellus) gilberti is a low-convexity species and shows marked lateral shape change, particularly in the genal region. Nephrolenellus geniculatus is more convex and shows less severe lateral shape change. Landmarks of both species exhibit an average trebling of the degree of scatter around their average ontogenetic trajectories in compacted samples. Because even well-preserved specimens in shales differ in shape from their precompactional appearance, results of morphometric studies utilizing metric distances between landmarks in trilobites where compaction can be detected must be interpreted with caution.

Preliminary Investigation of Mesh Stability for Linear Systems

1999 ◽  
Author(s):  
Pete Seiler ◽  
Aniruddha Pant ◽  
J. K. Hedrick
Keyword(s):  
Linear Systems ◽  
Mimo Systems ◽  
Preliminary Investigation ◽  
Two Dimensions ◽  
String Stability ◽  
Significant Research ◽  
Simple Class ◽  
The Subject ◽  
A Chain ◽  
The One

Abstract Damping of disturbances as they propagate through a chain of interconnected systems, termed string stability, has been the subject of significant research. In this paper, we investigate mesh stability, which is the two-dimensional extension of string stability. We review the key results used for string stability analysis and then generalize the conditions for MIMO systems. These results are then applied to a simple class of linear systems which form a mesh in two-dimensions. It is shown (as in the one-dimensional case) that communicating the velocity and acceleration of the lead vehicle to all subsystems is sufficient for mesh stability. This result is then verified by simulation.

Spatial Interaction

1993 ◽  
Author(s):  
Norman I. Badler ◽  
Cary B. Phillips ◽  
Bonnie Lynn Webber
Keyword(s):  
Two Dimensions ◽  
Three Dimensions ◽  
Interactive System ◽  
Input Device ◽  
Direct Manipulation ◽  
Good Correspondence ◽  
Articulated Figures ◽  
Reachable Workspace ◽  
Kinesthetic Feedback ◽  
A Chain

This chapter describes the basic architecture of the Jack interactive system. The primary tools available to the Jack user involve direct manipulation of the displayed objects and figures on the screen. With articulated figures, movement of one part will naturally affect the position of other parts. Constraints are used to specify these relationships, and an inverse kinematics algorithm is used to achieve constraint satisfaction. As a consequence of user actions, certain global postural manipulations of the entire human figure are performed by the system. This chapter presents the direct spatial manipulations offered in Jack and shows how constraints are defined and maintained. One particular application of the body constraints is included: the generation of the reachable workspace of a chain of joints. 3D direct manipulation is a technique for controlling positions and orientations of geometric objects in a 3D environment in a non-numerical, visual way. It uses the visual structure as a handle on a geometric object. Direct manipulation techniques derive their input from pointing devices and provide a good correspondence between the movement of the physical device and the resulting movement of the object that the device controls. This is kinesthetic correspondence. Much research demonstrates the value of kinesthetically appropriate feedback [Bie87, BLP78, Sch83]. An example of this correspondence in a mouse-based translation operation is that if the user moves the mouse to the left, the object moves in such a way that its image on the screen moves to the left as well. The lack of kinesthetic feedback can make a manipulation system very difficult to use, akin to drawing while looking at your hand through a set of inverting mirrors. Providing this correspondence in two dimensions is fairly straightforward, but in three dimensions it is considerably more complicated. The advantage of the direct manipulation paradigm is that it is intuitive: it should always be clear to the user how to move the input device to cause the object to move in a desired direction. It focuses the user’s attention on the object, and gives the user the impression of manipulating the object itself.

Oligosiloxanediols as building blocks for supramolecular chemistry: hydrogen-bonded adducts with amines form supramolecular structures in zero, one and two dimensions

2000 ◽  
Vol 56 (2) ◽  
pp. 273-286 ◽  
Author(s):  
Brian O'Leary ◽  
Trevor R. Spalding ◽  
George Ferguson ◽  
Christopher Glidewell
Keyword(s):  
Hydrogen Bonds ◽  
Supramolecular Chemistry ◽  
Building Blocks ◽  
Two Dimensions ◽  
Supramolecular Structures ◽  
Structural Motif ◽  
Two Dimensional ◽  
The Third ◽  
A Chain ◽  
Hydrogen Bonded

The structure of 1,1,3,3,5,5-hexaphenyltrisiloxane-1,5-diol–pyrazine (4/1), (C36H32O4Si3)4·C4H4N2 (1), contains finite centrosymmetric aggregates; the diol units form dimers, by means of O—H...O hydrogen bonds, and pairs of such dimers are linked to the pyrazine by means of O—H...N hydrogen bonds. In 1,1,3,3,5,5-hexaphenyltrisiloxane-1,5-diol–pyridine (2/3), (C36H32O4Si3)2·(C5H5N)3 (2), the diol units are linked into centrosymmetric pairs by means of disordered O—H...O hydrogen bonds: two of the three pyridine molecules are linked to the diol dimer by means of ordered O—H...N hydrogen bonds, while the third pyridine unit, which is disordered across a centre of inversion, links the diol dimers into a C 3 3(9) chain by means of O—H...N and C—H...O hydrogen bonds. In 1,1,3,3-tetraphenyldisiloxane-1,3-diol–hexamethylenetetramine (1/1), (C24H22O3Si2)·C6H12N4 (3), the diol acts as a double donor and the hexamethylenetetramine acts as a double acceptor in ordered O—H...N hydrogen bonds and the structure consists of C 2 2(10) chains of alternating diol and amine units. In 1,1,3,3-tetraphenyldisiloxane-1,3-diol–2,2′-bipyridyl (1/1), C24H22O3Si2·C10H8N2 (4), there are two independent diol molecules, both lying across centres of inversion and therefore both containing linear Si—O—Si groups: each diol acts as a double donor of hydrogen bonds and the unique 2,2′-bipyridyl molecule acts as a double acceptor, thus forming C 2 2(11) chains of alternating diol and amine units. The structural motif in 1,1,3,3-tetraphenyldisiloxane-1,3-diol–pyrazine (2/1), (C24H22O3Si2)2·C4H4N2 (5), is a chain-of-rings: pairs of diol molecules are linked by O—H...O hydrogen bonds into centrosymmetric R 2 2(12) dimers and these dimers are linked into C 2 2(13) chains by means of O—H...N hydrogen bonds to the pyrazine units. 1,1,3,3-Tetraphenyldisiloxane-1,3-diol–pyridine (1/1), C24H22O3Si2·C5H5N (6), and 1,1,3,3-tetraphenyldisiloxane-1,3-diol–pyrimidine (1/1), C24H22O3Si2·C4H4N2 (7), are isomorphous: in each compound the amine unit is disordered across a centre of inversion. The diol molecules form C(6) chains, by means of disordered O—H...O hydrogen bonds, and these chains are linked into two-dimensional nets built from R 6 6(26) rings, by a combination of O—H...N and C—H...O hydrogen bonds.

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.

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