Fig. 3. Relation among the dual vectors &, h, k and A. Fig. 2. Dual angle @ = @ + eq between the directed lines g and h. Fig. 4. Axes ps1, ps; of the pinion and the gear wheels, and the relative axis p32. where @ = @ + E@p denotes the dual angle made by é; and px, as illustrated in Fig. 4. From Eq. (5) the primal parts p3; and pz; are linearly independent. Hence, for any ¢ there is a choice of (@21, 31) € R’, as per Fig. 5, where 21, 3, and ¢~ are shown as related by the primal part of Eq. (6). Comparing the coefficients of ¢; and € reveals that Eq. (6) is equivalent to Fig. 6. Pliicker’s conoid = cylindroid. Fig. 8. Three-dimensional view of the Ball—Disteli diagram (« = 30°, % = 43.3 mm and R= 50 mm). Fig. 9. Three-dimensional view of Ball—Disteli diagram (% = 45°, a = R= 50 mm). With reference to the case of Fig. 8, the skew axes p., and p3, of the pinion 2, and gear 23, respectively, are assigned through the distance %) = 43.30mm and angle « = 30°. Consequently, the half diameter R of the cor- responding Pliicker conoid ¥ is equal to 50mm. The Ball—Disteli Diagram to analyze the relative screw motion between pinion and gear is obtained by referring to frame ¥(O;x),x2,x3) with the origin O symmet- rically located on the diameter of the conoid, the x,-axis making an angle « = 30° with both axes px and p31, respectively; the x3-axis is directed along the diameter of the conoid; finally, the x2-axis is orthogonal to the X,- and x3-axes. Fig. 10. General version of the Ball—Disteli diagram. Fig. 11. Distribution parameter dy of Pliicker’s conoid ¥. Under the condition 32 4 0, the inverse of 3, exists; we obtain, as per Eq. (16). Fig. 12. Distribution parameter 6 of the axodes of 23/22. Following Eq. (24) the distribution parameter of the axodes reads
