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RISOn the Matrix Realization of the Theory of Biquaternions
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: This paper describes a matrix algebra realization of Clifford’s theory of biquaternions. By examining 4 × 4 skew-symmetric matrices, the paper shows the connection between infinitesimal screws ...
Rational Bézier Line-Symmetric Motions
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: This paper brings together line geometry, kinematic geometry of line-symmetric motions, and computer aided geometric design to develop a method for geometric design of rational Bézier line-symmetric ...
On the Exact Representation of the Boundary Surfaces of the Swept Volume of a Cylinder Undergoing Rational Bézier and B-Spline Motions
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: This paper develops methods for the exact analysis and representation of the swept volume of a circular cylinder undergoing rational Bézier and B-spline motions. Instead of following the ...
Computer Aided Synthesis of Piecewise Rational Motions for Planar 2R and 3R Robot Arms
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: This paper deals with the problem of synthesizing piecewise rational motions of an object that satisfies kinematic constraints imposed by a planar robot arm with revolute joints. This paper ...
Computation of Spatial Displacements From Geometric Features
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: This paper develops the theoretical foundation for computations of spatial displacements from the simple geometric features of points, lines, planes, and their combinations. Using an oriented ...
Geometric Construction of Bézier Motions
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: This paper deals with discrete computational geometry of motion. It combines concepts from the fields of kinematics and computer aided geometric design and develops a computational geometric ...
Computation of Spatial Displacements from Redundant Geometric Features
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: This paper follows a previous one on the computation of spatial displacements (Ravani and Ge, 1993). The first paper dealt with the problem of computing spatial displacements from a minimum ...
Computer Aided Geometric Design of Motion Interpolants
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: 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 ...
Motion Interpolation With G2 Composite Bézier Motions
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: This paper deals with smooth motion interpolation. It presents two geometric algorithms for synthesizing composite Bézier motions with second-order geometric continuity (G2 ). The first one is ...
Computer Aided Geometric Design of Two-Parameter Freeform Motions
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: This paper brings together the notion of analytically defined two-parameter motion in Theoretical Kinematics and the notion of freeform surfaces in Computer Aided Geometric Design (CAGD) to develop ...