منابع مشابه
Singular Foci of Planar Linkages
The focal points of a curve traced by a planar linkage capture essential information about the curve. Knowledge of the singular foci can be helpful in the design of path-generating linkages and is essential to the determination of path cognates. This paper shows how to determine the singular foci of planar linkages built with rotational links. The method makes use of a general formulation of th...
متن کاملThe Geometry of Singular Foci of Planar Linkages
The focal points of a curve traced by a planar linkage capture essential information about the curve. In a previous paper, we showed how to determine the singular foci of planar linkages from an expression for the tracing curve derived by use of the Dixon determinant. This paper gives an alternative approach to finding the singular foci, one that lends itself to simple geometric interpretations...
متن کاملSemiconfiguration Spaces of Planar Linkages
This paper characterizes which subsets of Cn can be the set of positions of n points on a linkage in C. For example, assuming compactness they are just compact semialgebraic sets. Noncompact configuration spaces are semialgebraics sets invariant under the Euclidean group, with compact quotient.
متن کاملPlanar Linkages and Algebraic Sets
An abstract linkage is a one dimensional simplicial complex L with a positive number `(vw) assigned to each edge vw. A planar realization of an abstract linkage (L, `) is a mapping φ from the vertices of L to C so that |φ(v) − φ(w)| = `(vw) for all edges vw. We will investigate the topology of the space of planar realizations of linkages. You may think of an abstract linkage as an ideal mechani...
متن کاملGeometry and dynamics of planar linkages
In this article we present an approach to describing the geometry and curvature of the configuration spaces of a class of simple idealized planar linkages. This is based on determining the curvature of such configuration spaces canonically embedded into Euclidean space, and then the behaviour of the dynamics of such linkages can be understood via the associated geodesic flow. Our objective is t...
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ژورنال
عنوان ژورنال: Mechanism and Machine Theory
سال: 2004
ISSN: 0094-114X
DOI: 10.1016/j.mechmachtheory.2004.06.008