This calculator converts an entered arc-length difference at an entered reference radius into an equivalent central angle. A separate animation shows the defining inverse-cam topology: a crank-mounted roller driving a profiled groove in the follower.
Inverse Cam Interactive Calculator
Explore the exact circle identity theta=s/r and its unit conversions for an entered arc length and reference radius.
Equation Used
- Entered length s is distance measured along a circle of constant radius r.
- Radius and arc length use the same length unit.
- The result is a central-angle equivalent only.
- The animated crank roller and profiled-follower groove use a separate illustrative motion law.
- No manufacturable profile, roller-envelope offset, pressure angle, curvature/undercut, clearance, compliance, load, friction, dynamics, manufacturing tolerance stack or uncertainty model.
A radial, normal or machining profile deviation is not generally an arc-length deviation and cannot be mapped to output-angle error using e/r without local cam slope, follower geometry and kinematics. The animated groove is synthesized from an explicitly illustrative rocking law and is separate from the entered circle conversion.
Inverse-cam topology and separate circle conversion
An inverse cam, also called a profiled-follower mechanism, places a roller at the end of the driving crank inside a profiled groove on the driven follower. This reverses the familiar cam/follower roles.
The animation synthesizes an illustrative groove centerline for a simple rocking law and keeps the roller on that centerline. Separately, the calculator uses the exact circle identity s=r theta; the inputs do not define the animated groove.
Use as a geometry/unit check
The outputs can convert a known circular arc-length difference into angle at a known radius. They cannot predict the angular consequence of a cam-profile tolerance.
Why profile error is different
A cam profile error may be specified radially, normal to the surface, along a tool path or as contour deviation. Output error then depends on local surface normal, slope, curvature, follower and linkage geometry. The scalar s/r identity applies only when the entered length is truly circular arc length.
Worked example
An arc-length difference of 0.05 mm on a 25 mm reference circle equals 0.002 rad, 0.1146 degrees or 6.875 arcminutes. Arc-to-angle scale is 2.2918 degrees/mm at that radius.
Limits of the circle conversion
A cam-tolerance calculation needs the actual profile, follower arrangement and direction in which error is measured. Local slope, contact geometry and clearance affect how a profile deviation changes output position. The circular identity s/r supplies none of that information.
Questions
Can I enter radial profile error?
No. The input must be circular arc length for s/r to apply directly.
Is sensitivity constant over a real cam?
Not generally. Local kinematic sensitivity changes with geometry and position.
Is the animated groove a design?
No. It demonstrates the inverse-cam topology with an illustrative motion law and omits roller offset, pressure-angle and manufacturability checks.
References & Further Reading
- Wikipedia contributors. Cam. Wikipedia
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