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Abstract: In a variable-ratio rack and pinion steering, both the
pressure and skew angles of each rack tooth vary along its length within
the variable-ratio region of the rack. As a result, the teeth are both
curved along their length and changing in cross-section across the width
of the rack, and analytical solution of rack geometry becomes almost
impossible. A numerical method is proposed for direct numerical solution
of the rack geometry. With a given helical pinion and the required
variable-ratio transmission, geometry of the mating rack can be
computed, where solution of meshing equations is not needed. Numerical
results are 3D data of a large number of selected points on the contour
of the rack, being highly compatible with CNC machining. A computation
example is worked out, along which the proposed method is shown to work
well and the computational complexity is shown to be reasonable.
Key words: Meshing surfaces Variable-ratio transmission Rack and
pinion steering Numerical computation
CLC No: TH132.4
国家863计划资助项目(863-943-008).
Received 20010327, received in revised form 20010920
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