. Spons' dictionary of engineering, civil, mechanical, military, and naval; with technical terms in French, German, Italian, and Spanish . the equation hj 2 a/ (l — -), a ,du i . , ,s , to diameter a. When y = 0, ^ y expresses \ the circumference of the circle, and t the timeof descent through half the cycloid. Take c to represent ^ 0 to diameter a, c = t{).Take t = J, and consequently the time in the entire arc one second, c=^l^ {), c^ = l{a, d), 4c2 4c2 , 4c2 y d ; which may be put under the form d, \a = d. Take A M = 07, P M = y, Fig. 3354, Q N = 2 a, arc N P = ö,
. Spons' dictionary of engineering, civil, mechanical, military, and naval; with technical terms in French, German, Italian, and Spanish . the equation hj 2 a/ (l — -), a ,du i . , ,s , to diameter a. When y = 0, ^ y expresses \ the circumference of the circle, and t the timeof descent through half the cycloid. Take c to represent ^ 0 to diameter a, c = t{).Take t = J, and consequently the time in the entire arc one second, c=^l^ {), c^ = l{a, d), 4c2 4c2 , 4c2 y d ; which may be put under the form d, \a = d. Take A M = 07, P M = y, Fig. 3354, Q N = 2 a, arc N P = ö, ^ = AM = AN — NM = Ö — sin. 0 = ^y — ^ (2ay — y% the general expression for the normal is y v 1 + i — j, dx = j ■^ I d y si 2ay — y^ isl 2ay — y-) d X dy r (2 a - yf d y _ (2 ad X dy\ yf /dyy \dx) y^ (2 a 2a — y dy, yf 1 + \dx) y A^-m) (2 ay W 1 + m)-^^- An expression for the radius of curvature is -^ ;^—- ;• when p — -^ and q = -r—^ ; Ú Oj X CI X Take z ■=2a — y _ dy^ _z^ dx I 2 a y2 (2a-yy y^ z dz 1 _ 1z^ y ^dy dx y^ But dz dy, GUNNEKY. 1751 •^ - -^ 5 ^ dy = —dy = r^^y- y y 4:yz^y^. Substituting value for z, ^ = - 2y + 4a-2y^ ^^ ^ __4a _^^^. ^^^ ^^ 4y (2a - !/)^ Î/2 4^(2«-2/)^ (2 a —v)^ cPu a , (jPy a a ^ ^^ dy = j-^^ dx. Substituting this value iox dy, —^ = -dx,-— = 5 = 3- Substi- 2 ax y ax y tuting these values, ^ +-^ ^^ = L_^ . !_ ^ ^^ a^ y^ - 2 ^ 2^. Taking E to represent the radius of ciu-vature and N the normal, we have R = 2v2a2/, N = /\/2a?/; therefore it is evidentthat in this curve the radius of curvature is equal to twice the normal ; therefore at the vertex theradius of curvature is equal to twice the diameter of the generating circle. The involute of a semi-cycloid A 0 U, Fig. 3355, is an equal semi-cycloid U P V in an oppositedirection, the extremity of the base of the latter being in contact with the vertex of the any point O draw 0 B parallel to A C, cutting the generatingcircle in F, and joi
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Keywords: ., bookcentury1800, bookdecade1870, bookidsp, booksubjectengineering
