Pressure Angle is similar to Transmission-Angle.

Pressure-Angle represents the efficiency with which a cam transfers its motion and force to the follower, and vice versa.

Imagine pushing a door to open it...

•If you push the door-handle with a straight arm, with your arm at 90º to the door (perpendicular(⊥), or normal to the door), you will open the door easily. You only need to overcome the inertia force of the door and any friction in its hinges. You will not need to hold on to the door-handle.

•If you push the door-handle through a straight-arm, with your arm at an angle of 45º to the door, then you will need to:

oOvercome the inertia of the door - this is the same as before if the door opens with the same motion-law.

oPlus, you will need to hold on to the door-handle so that your hand does not slide across the door.

The Total Force against your hand will increase.

There is a force component from the door-handle that reacts against your hand to stop you hand sliding across the door. This force component is resisted by the door's hinges, which also pull/push on the door-frame.

The transmission angle with which your arm pushes against the door-handle is similar to the pressure-angle between a Cam-Profile and the Follower-Roller

The three vectors of the force-triangle (usually taken at the center of the Follower-Roller) that result from the contact between the Cam-Profile and the Follower-Roller are the:

•Contact Force. It is in the direction that is normal to the Cam-Profile at the contact-point between the Cam-Profile and Follower-Roller.

•Useful-Force.  It is in the direction is in which the Follower-Roller must move.

•Useless-Force. Its direction stretches a Rotating-Follower, or bends a Translating-Follower.

From the three vectors, we can define Pressure-Angle

The Pressure Angle, , is the angle from the direction in which the center-of the Follower-Roller must move to the direction of the contact-force acting through the center of the Follower-Roller.

Pressure Angle Limits: Rules-of-Thumb

To reduce the Pressure Angle

Force Vectors with different Pressure Angles

Compare Contact Force, Useful Force, and Useless Forces

Pressure Angle = 30º

Pressure Angle = 45º

Understanding Overturning-Moment

Imagine you want to slide a plank of wood along the floor, but between two walls. The plank is 2m long, 1m wide, and the 2m length is along the walls. There is a small gap.

The Plank is uniform. However, it is cut so that it contacts the wall only at its ends, 2m apart.

Ff (against the floor) = Friction-Coefficient (μ) × Mass × Gravity (mg).

Note: do not confuse Friction-Coefficient, μ, and Pressure-Angle, μ.

If the friction force is constant, the Friction-Force vector will be through the center-of-Mass and parallel to the wall - nominally 0.5m away from the wall.

No Over-turning Motion

If you slide the plank (slowly) with a hand that is in line with the center-of-mass, the plank will not tend to rotate.

In the ideal case, the wall does not need to react against the sides of the plank. The wall does not, theoretically, need to be there. Although it would be difficult to do without the walls!

IMPORTANT: ignoring Friction against the wall.

Overturning Moment

Now, push the plank at a point nearer to one wall (so that the contact is offset from the center-of-mass and friction-force vector.

Overturning Moment = Frictional force(Ff) × perpendicular distance to your hand from plank's center-of-mass 'axis'.

Assuming the Friction-Force does not change, the further away from the plank's center-of-mass you push, the greater the over-turning moment.

The overturning-moment will tend to rotate the plank. The wall prevents it rotating, of course.

Re-turning Moment (to coin a term)

The wall resists the plank at opposite corners of the plank (nominally)

Re-turning moment = Reaction Forces from the walls against the plank × length of plank

If you use a longer plank, the reaction-forces from the wall become less, but the returning-moment remains the same.

Over-turning moment = Re-turning moment

Over-turning moment = Contact-Force × distance to the 'sliding-axis' from the contact-point.

Re-turning moment = Reaction-Force at one end of the Sliding-Joint × distance between reaction forces in Sliding-Joint.

In the image: we can see the contact-force between a Cam-Profile and Flat-Faced Follower is 20N, and it is 50mm from the vertical sliding axis of the Translating-Follower.

Thus:

Overturning Moment = Contact Force (20N) × Distance to Contact Point from Sliding-Axis (50mm) = 1000N.mm

Overturning-Moment = Re-turning-Moment

Re-turning Moment (1000N.mm) = Distance between (or Length of) Sliding-Bearing(s) (40mm) × Reaction Force (25N)

Notes:

During a typical follower motion, the contact point continually moves across the flat-face from one side of the sliding-axis to the other.

This analysis ignores any friction-force in the sliding-bearings and friction-force between the Cam-Profile and the Flat-faced-Follower.

How to reduce the Over-turning Moment: