TY - JOUR

T1 - On the break-ups of spherical centre- and circle-point curves of the PP-PP case

AU - Lu, Deng Maw

AU - Chang, Chi Feng

AU - Hwang, Wen Miin

PY - 1996/8

Y1 - 1996/8

N2 - With a pole and two instant centres specified on a unit sphere, a geometrical construction is proposed to determine the spherical centre- and circle-points. The explicit equations of the corresponding spherical centre- and circle-point curves of the PP-PP case are thus obtained by using spherical trigonometry. All break-ups of these spherical centre- and circle-point curves are directly generated from the explicit equations. Through an exhaustive search, it was found that there are four kinds of degenerated curves, i.e. (1) two points and a great circle, (2) two spherical ellipses and a great circle, (3) three orthogonal great circles and (4) a sphere. Two design examples are presented.

AB - With a pole and two instant centres specified on a unit sphere, a geometrical construction is proposed to determine the spherical centre- and circle-points. The explicit equations of the corresponding spherical centre- and circle-point curves of the PP-PP case are thus obtained by using spherical trigonometry. All break-ups of these spherical centre- and circle-point curves are directly generated from the explicit equations. Through an exhaustive search, it was found that there are four kinds of degenerated curves, i.e. (1) two points and a great circle, (2) two spherical ellipses and a great circle, (3) three orthogonal great circles and (4) a sphere. Two design examples are presented.

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U2 - 10.1016/0094-114X(95)00102-5

DO - 10.1016/0094-114X(95)00102-5

M3 - Article

AN - SCOPUS:13644272890

VL - 31

SP - 749

EP - 762

JO - Mechanism and Machine Theory

JF - Mechanism and Machine Theory

SN - 0374-1052

IS - 6

ER -