Machine Kinematics
solved, then drawn
Concept

flat-faced follower — where it appears

A cam follower that touches the cam with a flat face instead of a roller, so the contact normal runs along its guide and its pressure angle is zero. What it asks instead is a convex cam, whose radius at the contact, R₀ + s + s″, stays positive.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

A flat face on a base circle of 30, where the profile bends tightest. The cycloidal programme — rise 10 over 120°, return over 120° — cut for a flat-faced follower on a base circle of 30, turned to 212.4°, where the profile's radius of curvature is smallest. The contact sits −5.37 from the follower's axis, which is ds/dθ, and the dashed circle is the one that fits the profile there: R₀ + s + s″ = 24.668, and 24.668 fitted through the drawn curve. The face's pressure angle is zero at every angle. What it needs instead is for that radius to stay positive, and it does so on every base circle above 5.332.

A flat face asks for a convex cam

A flat-faced follower is pushed at right angles to its face, so its pressure angle is zero at every angle and the constraint that sizes a roller's cam disappears. What replaces it is convexity: the profile's radius at the contact is R₀ + s + s″, and a base circle below 5.332 leaves a cycloidal cam with a hollow the face cannot reach — held 0.446 high on a base of 2.

cams · Cam A yoke 70 wide on a constant-breadth cam, at 60°. The cycloidal programme — rise 10 over 120°, return over 120° — cut for flat faces on a base circle of 30 and held between two parallel faces 70 apart, turned to 60.0°. The upper face rests at 5.000 above the base circle, which is the programme's lift there. The lower face touches the cam too: the distance across the cam along the follower's line is 70.000 at this angle and at every other, so the follower is driven up by one face and down by the other with no spring and nothing to spare.

A cam that holds its follower both ways

Two parallel faces joined into a yoke can drive a follower out and back with no spring, but only if the cam's breadth along the follower's line is the same at every angle — s(θ) + s(θ + 180°) constant. That makes the second half-turn the first one reflected. The cam field's standing programme misses by 9.502, and a second disc that frees the programme needs a yoke at least 60.66 wide.

cams · Cam A flat face on a swinging arm, and the cam it asks for. The cam a flat-faced follower needs when its face is carried on an arm pivoted 300 from the cam's centre, with a base circle of 20 and a lift of 20, drawn in the cam's own frame at three cam angles. The heavy line is the face, the dashed line is the perpendicular from the cam's centre to it, and the dot is the contact. Its distance from the foot of that perpendicular is the offset, which for a sliding face would be the programme's own velocity and here is a quantity with the arm in it. Over the turn it runs from -20.41 to 17.95, so the face must be 38.4 wide.

A flat face on an arm is worse

Carry a cam's roller on a swinging arm instead of a slide and the pressure angle improves — a long arm beats an offset. Carry a flat face on one and the opposite happens. The cam sees the sine of the follower's rotation rather than the rotation, and the distortion costs convexity: the smallest workable base circle rises from 10.66 on a slide to 28.68 at a pivot three base circles out, and below a certain arm length no base circle works at all.

cams · Cam

Named alongside it

The objects these essays reach for when they reach for this one.

Base circleConvex hullEnvelopeFollowerMotion lawPressure angleSupport functionAccelerationCam profileConjugate camconstant-breadth camDesign rule

All concepts