This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1915 Excerpt: ...(1 +m)tan-j. Now were m really zero this equation would give to f) a value equal to =--tan 1 tan--=at. c 2 Call this value 0O. Really it means the position of the crank at the instant determined by t if the angular velocity were strictly uniform and equal to a. 2 ( cd ) We may therefore write t) =--tan-1(l+rw) tan-j (3 ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1915 Excerpt: ...(1 +m)tan-j. Now were m really zero this equation would give to f) a value equal to =--tan 1 tan--=at. c 2 Call this value 0O. Really it means the position of the crank at the instant determined by t if the angular velocity were strictly uniform and equal to a. 2 ( cd ) We may therefore write t) =--tan-1(l+rw) tan-j (3) which is the solution. If, for example, c=l and m=--F 200 then 0=2 tan-111-005 tanj. From this we see that when 0O = 120, 0 becomes 2 tan-1! 1-005 tan 60 = 2 tan-1 (1-005 X 1-73205) = 2 tan-1 1-74071 = 2 X 60-12 = 120-24 or that the crank would be nearly degree ahead of its supposed position. It is useful to get an expression for this deviation directly. From (3) 6--0o=2 tan-l+m) tan--l--0O. If for example c = 1 and m =--, this equation gives the 25 maximum deviation = 2 tan-1--=2Xl-2=2-4 degrees. 50 B When m is much smaller than--, say equation (4) can 25 200 be approximately written: --2 TYb Yfh I-X--=---So that with c=l and m = the maxic 2 c 200 mum deviation would be 1 radian or 0-28 degree. 200 6 Equation (2) shows how the value of 6 can be calculated for any position of the ideal crank, and the deviation may have its most important effect electrically even when it has not itself its largest numerical value. For that reason it is desirable to have some means of calculating it easily. In cases in which it is only desired to find the maximum deviation to some approximate degree of accuracy, it is sufficient to take a mean value of the excess angular velocity and multiply it by the time during which it operates. Thus if as before c = 1 and m=2Q' caumg the angular velocity to, the average excess of angular velocity-2 co co--V 200100tt tT and this operates through 180 or for a time equal to-, so CO that the angular motion gained = m V--= 1 Io...
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