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Tham khảo tài liệu 'parallel manipulators new developments part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Asymptotic Motions of Three-Parametric Robot Manipulators with Parallel Rotational Axes 51 b Let c2 c3 0 at u . Then a motion through the point u is nontrivial asymptotic iff the revolute joint and only the prismatic joint whose axis is parallel to the axis of the revolute joint work. Proposition 5. Let TA3 be a robot of spherical rank 1 with two prismatic joints and let the directions of the joint axes be linear dependent at u t0 i.e. ã c2b2 c3b3. Then a The zero Coriolis acceleration is a necessary condition for the motion to be asymptotic at u t0 . b In the case that no two axes of joints are parallel at u a motion through the point u is nontrivial asymptotic iff all joints work and the joint velocities of the prismatic joints satisfy the relationship c2 c3 in the cases RTT TTR and -c2 c3 in the case TRT. c In the case that the axis of the revolute joint is parallel to one axis of a prismatic joint a motion is nontrivial asymptotic iff the revolute joint and only the prismatic joint whose axis is parallel to the axis of the revolute joint work. 3 Let us investigate asymptotic robot motions in a regular position when dimCA 2 and A3 u is not a subalgebra. Then CA n A3 u K span ã b3 B2 - ã b2 B3 i.e. the equation ã b3 b2 - ã b2 b3 k2 ãX b2 k3 ãX b3 k2 k3 e R is valid. In this case the motion is asymptotic at the point u if and only if a 1 for RTT W1W2 0 X m2 w1w3 0 ã X m3 Ẳ 0 k2 ã X m2 k3 ã X m3 Ảe R i.e. ii1ii2 k2Ằ ÍŨ1ŨÍ3 k3Ằ a 2 for TRT w1w2 0 ã X mi u2u. 0 ãX m3 Ẳ 0 k2 ã X m3 k3 ã X m3 Ảe R i.e. ii1ii2 k2Ằ u2u3 k3Ằ a 3 for TTR ii1ii3 0 ã X m1 03 0 ãX m2 Ẳ 0 k2 ã X m1 k3 ã X m2 Ảe R i.e. u1u3 k2Ằ u2u3 k3Ằ . We summarize the previous results. Proposition 6. Let TA be a robot of spherical rank 1 with two prismatic joints and let the directions of the joint axes be independent at t0 i.e. ã c2b2 c3b3. Then A motion is nontrivial asymptotic at t0 iff joint velocities at t0 satisfy uu I2 k2Ằ uu I3 k. . for RTT upp k2Ằ u2u3 k. . for TRT and for TTR uup k2Ằ u2u3 k. . .
