2015
DOI: 10.1080/0951192x.2015.1034783
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Using geometric algebra to represent and interpolate tool poses

Abstract: In conventional computer aided manufacturing techniques, a tool path is sent to the machine tool controller as a sequence of precision points. This means that errors are introduced when the controller interpolates between the points to recover the intended path. For 4-and 5-axis machining, a sequence of precision poses (positions and orientations) is needed. The use of geometric algebra in representing poses is discussed. The form of algebra used can represent rigidbody transforms exactly and can interpolate, … Show more

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Cited by 6 publications
(6 citation statements)
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“…The version used here is called G 4 . This is discussed in greater detail elsewhere [3,23,24] and what follows here is an overview of its construction. The G 4 version is used here since the purpose of this paper is to investigate its properties which are different from other versions of geometric algebra: in particular and importantly, as discussed in Sect.…”
Section: Geometric Algebra Gmentioning
confidence: 99%
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“…The version used here is called G 4 . This is discussed in greater detail elsewhere [3,23,24] and what follows here is an overview of its construction. The G 4 version is used here since the purpose of this paper is to investigate its properties which are different from other versions of geometric algebra: in particular and importantly, as discussed in Sect.…”
Section: Geometric Algebra Gmentioning
confidence: 99%
“…The typical vector in G 4 is the element p = W e 0 + Xe 1 + Y e 2 + Ze 3 . This is used to represent the point (W, X, Y, Z) in the projective space R((ε)) 3 , and the point (X/W, Y /W, Z/W ) in RP((ε)) 3 . By letting ε become zero, it also represents a point in Euclidean space R 3 , assuming that the components remain finite.…”
Section: Points and Planesmentioning
confidence: 99%
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“…The tool trajectory is approximated by segments of the screw line [15]. More precisely, it is not a trajectory, what is approximated, but a function that determines the motion of a rigid body in space by a sequence of screw motions.…”
Section: First Stepmentioning
confidence: 99%
“…In specifying free-form motions, one approach is to deal separately with the (translational) motion of a reference point in the moving body and the (rotational) motion of the body with respect to it [20,21,22]. An alternative is to handle the motion of the body as a single variable transform [5,23,24].…”
Section: Introductionmentioning
confidence: 99%