Automatic Sketching of Planar Kinematic Chains

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Mechanism and Machine Theory

Automatic Sketching of Planar Kinematic Chains

Belfiore, N.P., Pennestrì, E.,

Pergamon Press Ldt., Vol. 29, Issue 1, Jan. 1994, pp. 177 - 193,

DOI: 10.1016/0094-114X(94)90029-9

Abstract

In this paper an original method for the fully automatic sketching of planar kinematic chains is described. This procedure may ease the interpretation of the results obtained during the enumeration of complex multi-loop kinematic chains. The designer is supplied with a graphical interface useful to better understand the topological properties of the kinematic chain generated, by a confortable visual inspection. The sketch of a kinematic chain is obtained by first mapping the graph in the plane and then sketching its line-graph, after deletation of extraneous edges. The graph is embedded in the plane utilizing a baricentric procedure. The informations included in the topological embedding of the graph directly leads to the deletation of the extraneous edges of the line-graph. Likewise, a straightforward original procedure converts the embedded edges of the graph into embedded vertices of the line-graph. A fully automatic drawing of the complete atlas of 1 d.o.f. planar kinematic chains with eight and ten links was obtained without any occurrence of crossing links. Finally several examples are illustrated and some further developments discussed.

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