By Mark W. Spong

ISBN-10: 0471649902

ISBN-13: 9780471649908

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Extra resources for Robot Modeling and Control

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28 Diagram for Problem 1-15 while a rotational link would travel through an arc length θ as shown. Using the law of cosines show that the distance d is given by d= 2(1 − cos(θ)) which is of course less than θ. With 10-bit accuracy and = 1m, θ = 90◦ what is the resolution of the linear link? of the rotational link? 28. If the length of the link is 50 cm and the arm travels 180? what is the control resolution obtained with an 8-bit encoder? 15 assuming that the 8-bit encoder is located on the motor shaft that is connected to the link through a 50:1 gear reduction.

17) is the composition law for rotational transformations. It states that, in order to transform the coordinates of a point p from its representation COMPOSITION OF ROTATIONS z1 z0 z1 , z2 φ z1 , z2 + y0 , y1 Fig. 9 z0 = x0 x1 43 x1 θ x2 y2 y1 x0 φ x1 y2 θ y0 , y1 x2 Composition of rotations about current axes. p2 in the frame o2 x2 y2 z2 to its representation p0 in the frame o0 x0 y0 z0 , we may first transform to its coordinates p1 in the frame o1 x1 y1 z1 using R21 and then transform p1 to p0 using R10 .

REPRESENTING POSITIONS 31 Since the origin of a coordinate system is just a point in space, we can assign coordinates that represent the position of the origin of one coordinate system with respect to another. 5 In cases where there is only a single coordinate frame, or in which the reference frame is obvious, we will often omit the superscript. This is a slight abuse of notation, and the reader is advised to bear in mind the difference between the geometric entity called p and any particular coordinate vector that is assigned to represent p.

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Robot Modeling and Control by Mark W. Spong

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