A face cam uses a groove or surface on the end face of a rotating member to prescribe follower motion. This page models one explicitly defined axial displacement schedule at a constant pitch radius; it does not assign universal tolerances, life, accuracy, loads or speed limits.
Face Cam Interactive Calculator
Explore a symmetric cycloidal rise-dwell-return schedule and its ideal pitch-circle groove angle, follower speed and follower acceleration.
Equation Used
- Constant pitch radius and constant cam angular speed.
- Symmetric cycloidal rise and return with equal remaining dwells.
- Rigid form-closed groove centreline with no roller-envelope or cutter offset.
- No force, torque, contact stress, clearance, lubrication, strength, fatigue, resonance or safe-speed model.
Educational kinematics only. The unwrapped centreline does not include roller-radius offset, groove width, cutter compensation, contact stress, clearance, lubrication, flexibility, manufacturing tolerances or a safe operating speed.
Form-closed face groove
The cam rotates while a guided follower reads a groove or surface on its end face. In a form-closed arrangement, a roller is constrained by both sides of the groove, so the geometry prescribes rise and return without requiring a spring solely to maintain contact.
The animation shows two coordinated views: cam phase on the face and the same groove centreline unwrapped around the entered pitch radius. The unwrapped plot makes the defined axial displacement schedule explicit.
Where cam-controlled motion is useful
Cams are used when a repeatable displacement schedule must be generated from rotation. Form-closed grooves are used in machinery where the follower must be geometrically constrained in both directions. Suitability still depends on the complete mechanism, loading, roller and groove geometry, materials, lubrication and manufacturing method.
Defined cycloidal schedule
During a rise of angular width beta, let u=theta/beta. The chosen displacement is s=H[u-sin(2pi u)/(2pi)]. Its first derivative is ds/dtheta=(H/beta)[1-cos(2pi u)] and its second derivative is d²s/dtheta²=(2pi H/beta²)sin(2pi u). The return uses the symmetric reverse relation.
The peak slope is 2H/beta. On an ideal pitch circle of radius R, the unwrapped groove-slope angle is atan(|ds/dtheta|/R). Multiplying the first derivative by cam angular speed gives follower velocity. Multiplying the second derivative by angular speed squared gives follower acceleration.
Reading the calculator
The entered rise angle is also used for the return. The unused rotation is split into equal high and low dwells, so each dwell is 180 degrees minus the rise angle. Increasing stroke or shortening the rise raises slope, speed and acceleration; increasing pitch radius reduces the ideal groove-slope angle without changing the displacement schedule.
Scope and limitations
This is a centreline kinematic construction, not a manufacturable cam specification. A real design requires roller-radius and cutter offsets, groove width and depth, curvature and undercut checks, contact forces, shaft and bearing reactions, material and lubrication choices, tolerances, dynamic response and a verified speed limit.
Questions
Does the displayed groove angle equal a universal pressure-angle limit?
No. It is the local slope angle of the ideal unwrapped centreline. Actual contact geometry and acceptable limits depend on the follower and groove design.
Why use cycloidal motion?
It provides zero velocity and zero acceleration at the rise and return boundaries for this ideal constant-speed schedule. It does not eliminate dynamic loads within the motion interval.
Does the model prove the cam can run at the entered rpm?
No. RPM only converts geometric derivatives to ideal velocity and acceleration.
Academic references
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