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A means has been discovered to apply gear pairing to create a one degree of freedom open-loop spatial mechanism. A specially chosen geometry consisting of three pairs of parallel joint axes is constricted by five sets of gears, three of which are parallel planar, allows for a reconfigurable mechanism that is suited for repetitive tasks. Previous work has examined three-dimensional rigid body guidance in closed-loop geared mechanisms, but has not come to a solution for the open-loop case. Gear pairs are designed based upon a desired position and orientation path for the end effector. Numerical optimization is performed to obtain physically realizable gear profiles. Non-circular gear centrodes must be continuous and smooth as well as mono-directional, that is, gear ratios of a given pair may not switch signs. These constraints eliminate non-realizable or non-optimal gears in favor of simple, more easily produced profiles. Variable parameters include link lengths, joint offsets and twist angles. Numerical examples are presented.Copyright © 2009 by ASME |