Differential Kinematics of Spherical and Spatial Motions Using Kinematic Mapping

1986 ◽  
Vol 53 (1) ◽  
pp. 15-22 ◽  
Author(s):  
J. M. McCarthy ◽  
B. Ravani
Keyword(s):  
Geodesic Curvature ◽  
Intrinsic Properties ◽  
Mechanism Synthesis ◽  
Basic Framework ◽  
Kinematic Mapping ◽  
Curvature And Torsion ◽  
Spherical Mechanism ◽  
Spatial Kinematics

This paper develops the basic framework for studying differential kinematics of spherical and spatial motions using a mapping of spatial kinematics. Relationships are derived relating the intrinsic properties of the image curves corresponding to a mapping of spherical and spatial kinematics and the instantaneous invariants of the corresponding spherical and spatial motions. In addition, in the case of spherical motions, the equations for the inflection cone and cubic cone of stationary geodesic curvature, important in spherical mechanism synthesis, are derived in terms of the curvature and torsion of corresponding image curves. Similar relationships defining the polhodes of spherical motions and their curvature at the reference instant are recast as well. A simple example involving a special spherical four-bar motion is also presented.

scholarly journals Spherical Mechanism Synthesis in Virtual Reality

1998 ◽  
Author(s):  
Todd J. Furlong ◽  
Judy M. Vance ◽  
Pierre M. Larochelle
Keyword(s):  
Virtual Reality ◽  
Design Space ◽  
Three Dimensional ◽  
Mechanism Synthesis ◽  
Kinematic Synthesis ◽  
New Approach ◽  
Spherical Mechanisms ◽  
Input Design ◽  
Previous Design ◽  
Spherical Mechanism

Abstract This paper presents a new approach to using virtual reality (VR) to design spherical mechanisms. VR provides a three dimensional design space where a designer can input design positions using a combination of hand gestures and motions and view the resultant mechanism in stereo using natural head movement to change the viewpoint. Because of the three dimensional nature of the design and verification of spherical mechanisms, VR is examined as a new design interface in this research. In addition to providing a VR environment for design, the research presented in this paper has focused on developing a “design in context” approach to spherical mechanism design. Previous design methods have involved placing coordinate frames along the surface of a constraint sphere. The new “design in context” approach allows a designer to freely place geometric models of movable objects inside an environment consisting of fixed objects. The fixed objects could either act as a base for a mechanism or be potential sources of interference with the motion of the mechanism. This approach allows a designer to perform kinematic synthesis of a mechanism while giving consideration to the interaction of that mechanism with its application environment.

The Image of the Coupler Motion of a Special Spherical Four Bar Linkage

1987 ◽  
Author(s):  
J. M. McCarthy
Keyword(s):  
Rational Functions ◽  
Global Properties ◽  
Kinematic Mapping ◽  
Curvature And Torsion ◽  
Four Bar Linkage ◽  
Spherical Motion

Abstract This paper uses a kinematic mapping of spherical motion to derive an image curve which represents the coupler motion of a doubly folding spherical four bar linkage. The image curve of this linkage, the so called “kite” linkage, can be parameterized by rational functions. This parameterization is presented as well as formulas which allow the computation of its curvature and torsion at any point. These formulas provide a link between the global properties of the coupler motion as represented by the image curve itself and its instantaneous properties given by the curvature and torsion functions.

scholarly journals A note on the ruled surface

1937 ◽  
Vol 30 ◽  
pp. i-ii
Author(s):  
R. Wilson
Keyword(s):  
Mean Curvature ◽  
Geodesic Curvature ◽  
Ruled Surface ◽  
Local Geometry ◽  
Parametric Curves ◽  
The Mean ◽  
Curvature And Torsion ◽  
Asymptotic Lines ◽  
Special Case ◽  
Elegant Form

The generators and their orthogonal trajectories form, perhaps, the most useful set of parametric curves for the study of the local geometry of a ruled surface. It is not generally realised, however, that the fundamental quantities of the surface can be expressed quite simply in terms of the geodesic curvature, the geodesic torsion and the normal curvature of the directrix, that particular orthogonal trajectory which is chosen as base curve. Certain of the results are similar in form to those arising in the special case of a surface which is generated by the principal normals to a given curve, except that the curvature and torsion are geodetic. In addition it is possible to obtain in an elegant form the differential equation of the curved asymptotic lines and the expression for the mean curvature.

Computer Aided Geometric Design of Motion Interpolants

1991 ◽  
Author(s):  
Q. J. Ge ◽  
B. Ravani
Keyword(s):  
Computer Animation ◽  
Three Dimensional ◽  
Geometric Design ◽  
Computer Aided Geometric Design ◽  
Mapping Space ◽  
Three Dimensional Objects ◽  
Computer Aided ◽  
Point Interpolation ◽  
Curvature And Torsion ◽  
Spatial Kinematics

Abstract This paper studies continuous computational geometry of motions and develops a method for Computer Aided Geometric Design (CAGD) of motion interpolants. The approach uses a mapping of spatial kinematics to convert the problem of interpolating displacements to point interpolation in the space of the mapping. To facilitate the point interpolation, the previously non-oriented mapping space is made orientable. Methods are then developed for designing spline curves in the mapping space with tangent, curvature and torsion continuities. The results have application in computer animation of three dimensional objects used in computer graphics, computer vision and simulation of mechanical systems.

Computer Aided Geometric Design of Motion Interpolants

1994 ◽  
Vol 116 (3) ◽  
pp. 756-762 ◽  
Author(s):  
Q. J. Ge ◽  
B. Ravani
Keyword(s):  
Computer Animation ◽  
Three Dimensional ◽  
Geometric Design ◽  
Computer Aided Geometric Design ◽  
Mapping Space ◽  
Three Dimensional Objects ◽  
Spline Curves ◽  
Computer Aided ◽  
Curvature And Torsion ◽  
Spatial Kinematics

This paper studies continuous computational geometry of motion and develops a method for Computer Aided Geometric Design (CAGD) of motion interpolants. The approach uses a mapping of spatial kinematics to convert the problem of interpolating displacements to that of interpolating points in the space of the mapping. To facilitate the point interpolation, the previously unorientable mapping space is made orientable. Methods are then developed for designing spline curves in the mapping space with tangent, curvature and torsion continuities. The results have application in computer animation of three-dimensional objects used in computer graphics, computer vision and simulation of mechanical systems.

The Image Curve of the Coupler of a Special Spherical Four Bar Linkage

1988 ◽  
Vol 110 (3) ◽  
pp. 276-280
Author(s):  
J. M. McCarthy
Keyword(s):  
Rational Functions ◽  
Global Properties ◽  
Kinematic Mapping ◽  
Curvature And Torsion ◽  
Four Bar Linkage ◽  
Spherical Motion

This paper uses a kinematic mapping of spherical motion to derive an image curve which represents the coupler motion of a doubly folding spherical four bar linkage. The image curve of this linkage, the so called “kite” linkage, can be parameterized by rational functions. This parameterization is presented as well as formulas which allow the computation of its curvature and torsion at any point. These formulas provide a link between the global properties of the coupler motion as represented by the image curve itself and its instantaneous properties given by the curvature and torsion functions.

The Instantaneous Kinematics of Line Trajectories in Terms of a Kinematic Mapping of Spatial Rigid Motion

1987 ◽  
Vol 109 (1) ◽  
pp. 95-100 ◽  
Author(s):  
J. M. McCarthy
Keyword(s):  
Rigid Motion ◽  
Distribution Parameter ◽  
Spatial Motion ◽  
Euler Parameters ◽  
Kinematic Theory ◽  
Unit Hypersphere ◽  
Kinematic Mapping ◽  
Curvature And Torsion ◽  
Curve Form

The dual Euler parameters of a rigid spatial motion are used to define a curve on a dual unit hypersphere. The dual velocity, curvature, and torsion of this curve form a set of instantaneous parameters related to the instantaneous invariants of the motion. In this paper these new parameters are used to reformulate the kinematic theory of line trajectories. The distribution parameter, Disteli formulas, and the inflection congruence are examined in detail.

Path Synthesis of Defect-Free Spatial 5-SS Mechanisms Using Machine Learning

2020 ◽  
Author(s):  
Shashank Sharma ◽  
Anurag Purwar
Keyword(s):  
Machine Learning ◽  
Learning Algorithm ◽  
Path Generation ◽  
Intrinsic Properties ◽  
Space Curves ◽  
Spatial Mechanisms ◽  
Variational Autoencoder ◽  
Newton Raphson ◽  
Curvature And Torsion ◽  
Path Synthesis

Abstract The synthesis of spatial mechanisms for defect-free path generation has not received a lot of attention. In this paper, we focus on the synthesis of 5-SS mechanisms and use a machine learning based approach. First, we create a coupler path database using a solver based on the iterative Newton-Raphson optimization algorithm. Subsequently, a data cleanup, normalization, balancing, and augmentation pipeline is established based on intrinsic properties of space curves namely curvature and torsion. Finally, we use an unsupervised learning algorithm based on Variational Autoencoder combined with K-means clustering to find a multiplicity of defect-free 5-SS mechanisms and examples are presented.

scholarly journals Spherical Mechanism Synthesis in Virtual Reality

1999 ◽  
Vol 121 (4) ◽  
pp. 515-520 ◽  
Author(s):  
T. J. Furlong ◽  
J. M. Vance ◽  
P. M. Larochelle
Keyword(s):  
Virtual Reality ◽  
Design Space ◽  
Three Dimensional ◽  
Mechanism Synthesis ◽  
Kinematic Synthesis ◽  
New Approach ◽  
Spherical Mechanisms ◽  
Input Design ◽  
Previous Design ◽  
Spherical Mechanism

This paper presents a new approach to using virtual reality (VR) to design spherical mechanisms. VR provides a three-dimensional (3-D) design space where a designer can input design positions using a combination of hand gestures and motions and view the resultant mechanism in stereo using natural head movement to change the viewpoint. Because of the three-dimensional nature of the design and verification of spherical mechanisms, VR is examined as a new design interface in this research. In addition to providing a VR environment for design, the research presented in this paper has focused on developing a “design in context” approach to spherical mechanism design. Previous design methods have involved placing coordinate frames along the surface of a constraint sphere. The new “design in context” approach allows a designer to freely place geometric models of movable objects inside an environment consisting of fixed objects. The fixed objects could either act as a base for a mechanism or be potential sources of interference with the motion of the mechanism. This approach allows a designer to perform kinematic synthesis of a mechanism while giving consideration to the interaction of that mechanism with its application environment.

Becoming Present, Becoming Absent: Movement and Visual Form in the Film Adaptation of Comédie

2012 ◽  
Vol 21 (2) ◽  
pp. 157-180
Author(s):  
David Foster
Keyword(s):  
The Other ◽  
Film Adaptation ◽  
Visual Form ◽  
Sergei Eisenstein ◽  
Basic Framework ◽  
Global Movement ◽  
Local Movement

This article examines the use of movement and visual form in the film adaptation of Samuel Beckett's Comédie (Marin Karmitz, 1966). The article broaches the kinetic elements of the work through addressing the manner in which the diegetic motion of the film can be seen to reflect extra-diegetic cinematic processes. The sense of movement that is created through Comédie's montage is then considered at length, making use of work on this theme by two quite different (though tangentially related) theorists: Sergei Eisenstein and Jean-François Lyotard. The article then charts the film's different manifestations of formal movement, and a basic framework is proposed to explain the manner in which the film creates moments of intensity, through what is termed the ‘local movement’ of the montage, and the manner in which the film manifests an overall curve of intensity, through what is termed the montage's ‘global movement’. It is argued that each form of montagic motion is reflected in the other, and that ultimately these movements might be seen to dramatise a human drive towards, and a concomitant flight from, an impossible state of ontological totality.

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