Cam_follower

# Cam_follower - It thus follows that the following equation...

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C Minimal radius of the cam L Distance from A to point of contact B ( ) θ f Follower displacement ( ) f C R + = (1) C R O A () f C A L B The problem of cam design Definitions The problem of cam design may be formulated as follows: Given: f ( ), f ( ) = f (2 π ) = 0 , Find: C MIN , L MIN , and the coordinates x - y of the cam profile such that the motion of the follower would be f ( ) From the figures we see that

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A L B C R θ x () y x , 1 y 2 y 2 1 y y y + = sin sin cos 2 1 y y x R + + = sin cos y x R + = sin cos cos 2 1 x y y L + = cos sin y x L + = d dR L = f d df L = sin cos y x f C + = + cos sin y x f + = ( ) cos sin f f C y + + = ( ) sin cos f f C x + = ( ) f C R + = (1) But So we have from 2 and 3 We carry equation 1 from the previous page From the figure we have It follows from 5 and 6 that ( ) f L = max min The parametric equations of the cam and the minimal (half) length of the follower face (2) (3) (4) (5) (6) (7) Design equation (8) Substituting 1 and 7 in 5 and 6 gives (9) (10) By solving 9 and 10 for x and y we obtain the parametric equations of the cam
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Unformatted text preview: It thus follows that the following equation must be satisfied for all Design equations (11) (12) A condition for avoiding cusp in the cam profile cusp By substituting 11 and 12 in 13 we find that in order to avoid cusp in the profile of the cam the following equation must be satisfied for all θ If there is a point of cusp in the cam then the contact between the cusp and the follower is not instantaneous. Therefore the mathematical condition describing the existence of a cusp is that for some = = d dy d dx ( ) ( ) > ′ ′ + + f f C (13) Design equation (14) for all...
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Cam_follower - It thus follows that the following equation...

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