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: Rack and pinion steering, Meshing surfaces, Numerical computation, Variable-ratio transmission