Shape design using intrinsic geometry

The present work outlines a methodology of shape synthesis using intrinsic geometry concepts for engineering design of two-dimensional and three-dimensional curves as well as three-dimensional surfaces. Using concepts of intrinsic geometry of curves, the shape of a curve can be defined in terms of intrinsic parameters such as the curvature and torsion as a function of the arc length. The method of shape synthesis proposed here consists of selecting a shape model, defining a set of shape design variables and then evaluating the Cartesian coordinates of a curve. It is assumed that the end-point coordinates and tangents are specified for design of curves. A shape model is conceived as a set of continuous piecewise linear segments of the curvature, each segment defined as a function of the arc length. The shape design variables are the values of curvature and/or arc length at some of the end-points of the linear segments. The proposed method of shape synthesis is general in nature. It has been shown how this method can be used to find the optimal shape of planar and spatial Variable Geometry Truss (VGT) manipulators for pre-specified position and orientation of the end-effectors. It is expected that the proposed methodology could be used for problems of shape optimization. The shape design of a three-dimensional curve is accomplished by modeling it as a generalized helix. The base of the helix lies in a plane perpendicular to the skew direction between the end-point tangents. The base curve is designed as a planar curve consisting of a set of linear curvature segments. The gradient of the helix can be modeled by choosing any one of the following three curves: (i) a parabolically blended curve, (ii) a cubically blended curve and (iii) a pair of Bezier curves. The proposed method has been shown to be useful for designing the shape of a Variable Geometry Truss-type manipulator. The method can also be used for a variety of other applications such as the path of a manipulator end-effector, or the geometry of a highway clover loop. A three-dimensional surface is considered as a surface swept by a generatrix curve when it moves along a directrix curve. In the present work a generatrix curve is considered to be a planar curve and it is defined using the intrinsic geometry concepts of shape models and shape variables. Four different types of surfaces have been proposed. (i) linearly swept surfaces, (ii) surfaces of revolution, (iii) generalized swept surfaces and (iv) transition surfaces. In each case, the generatrix can have a variable shape as it moves along the directrix. The proposed approach has been found suitable for modeling deformed geometries such as fabric drape surfaces. By controlling the variation of the shape design variables of the generatrix curve, it has been found that the proposed definition of surfaces can be used to design variable-shape three-dimensional surfaces. The present work is an attempt to develop definitions of planar curves, space curves and surfaces which are based on the intrinsic geometry concepts. It has been found that in engineering analysis and design-optimization work, an engineer is able to represent and manipulate the shape effectively using an intrinsic form of geometry as compared to a parametric form.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mechanical Engineering

Department dc:contributor.department

Mechanical Engineering

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1991

Author dc:creator

• Tavakkoli, Shahriar

Chairs dc:contributor.committeechair

• Dhande, Sanjay G.
• Reinholtz, Charles F.

Committee members dc:contributor.committeemember

• West, Robert L.
• Robertshaw, Harry H.
• Hendricks, Scott L.

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

etd-09202005-091004

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/39421