ANALYSIS OF THE QUICK-RETURN MOTIONS OBTAINED BY SLIDER CRANK CHAIN

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Referring to the quick return motions obtained by slider crank chain such as crank and slotted lever or Whitworth quick-return motion mechanism, the displacement χ of the body to which a quick return motion is to be given can be expressed conveniently in terms of the angle θ over which the driving pin has turned round. If the angular velocity of the driving pin be known the expression of the velocity and of the acceleration of the said body can be derived from that of χ by successive differentiations. These expressions remain the same so far as the ratio m of the radius of the driving pin circle to the length of the fixed link is constant. The length of stroke, the mean velocity, the maximum velocity, the ratio of cutting to return speed etc. of the reciprocating body can be plotted as curves on a base of m. These curves show the characteristics of the quick return motions. When m is greater than unity the expression of χ and accordingly those of the velocity and the acceleration, apply to the crank and slotted lever mechanism and if m is less than unity the same expressions apply to the Whitworth quick-return motion mechanism. The angular velocity of the driving pin of a crank and slotted lever mechanism may be made variable throughout one complete revolution of the pin, by means of the Whitworth mechanism as in the shaping machine of Mammutwerke in Nuernberg. The same expressions serve readily to show the advantages of the motion obtained by this combination of mechanisms.