Oblique circular torus, Villarceau circles and four types of Bennett linkages
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Cites background or methods from "Oblique circular torus, Villarceau ..."
...Using the toroid as a generated surface the existence of several overconstrained linkages can be explained: The Bennett 4R linkage [52, 53, 54, 55], the Myard 5R linkage [23] and the family of overconstrained 5R loops with two consecutive parallel axes presented by...
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...It is well known [52, 53, 54] that a Bennett linkage can be explained as a generator of a toroid where E is confined to move in a Villarceau circle by means of link between E and a revolute joint that generates the circle....
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4 citations
Cites background from "Oblique circular torus, Villarceau ..."
...Recently, a new geometric derivation of four types of Bennett 4R linkages [13] was done by considering RRS open chains whose spherical S joint center moves on the same oblique circular torus (OCT)....
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...properties of symbolic notations :(b,;a), (a,;b), (b,-;a) and (a,-; b) respectively can produce the same given oblique circular torus [13]....
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...An equilateral isogram is an achiral object and only one type of equilateral Bennett mechanism exist [13] when one ignores the partitioned mobility with the bifurcation toward two modes of rotation about aligned axes [14]....
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...The four types of Bennett mechanisms are degenerated into only two types [13]....
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3 citations
References
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"Oblique circular torus, Villarceau ..." refers background in this paper
...Substituting the relations of equation (9) into equation (8) leads to the algebraic equation of OCT with respect to the x-y-z system, which is...
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...Equation (8) expresses the Cartesian equation of OCT in the fixed X-Y-Z coordinate system that is the frame (O, i, j, k)....
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...The surface modeled by equation (8) is an OCT....
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