Conjugate cams are paired profiles fixed to one shaft and acting on followers connected to the same output. They can constrain the output in both directions without relying on a return spring. This page uses an explicitly defined pair of convex cams and opposed flat follower faces to demonstrate geometric closure, clearance and interference.
Conjugate Cam Interactive Calculator
Explore a defined flat-faced conjugate-cam pair. Set the distance between opposing follower faces, the two mean cam support distances and a requested clearance. The animation distinguishes zero-gap closure, free play and interference.
Equation Used
- Two convex cams keyed together on one shaft, each contacting one of two rigidly connected flat follower faces.
- The support-function example is h1(phi) = R1 + A cos(2phi) + B cos(phi), h2(phi) = R2 − A cos(2phi) + B cos(phi), with A = 0.05 min(R1,R2) and B = 0.12 min(R1,R2).
- The faces translate together. Their opposing support distances always sum to R1 + R2. No roller-radius correction is involved.
- With nonzero gap the pictured pose follows the primary cam only; actual free-play motion depends on load. Negative gap is a geometry preview, not runnable motion.
This example uses flat followers, not rollers. Mean support distances define the illustrated convex profiles. Compare the signed gap with your requested clearance. Choose practical tolerance limits using the actual loads, materials and manufacturing process.
Two cams, one shaft, one output
The blue primary cam and gold return cam rotate together in separate axial planes on a common shaft. The axial spacing is exaggerated in the view so both profiles and their contact points can be seen. The two green follower faces belong to one rigid yoke constrained by fixed slide guides.
The primary cam sets the upper face height in the preview. For the matched zero-gap geometry, the return cam touches the lower face at the same time, and the yoke is geometrically constrained through the cycle. Each surface pushes its own follower; a cam contact is not a tensile connection.
With positive gap, the lower face is separated in this primary-contact preview. A real mechanism can move within that clearance depending on its load. With negative gap, the selected parts overlap; the page keeps the geometry visible and marks interference instead of claiming the mechanism can run.
The illustration uses flat faces so its closure condition can be derived exactly from support distances. A roller-follower design needs roller radii, offsets and its actual motion law. Those variables are not supplied here.
Positive geometric constraint
Conjugate cam arrangements are useful for explaining mechanically constrained return motion. MechDesigner’s cam documentation describes multiple cam profiles driving followers mounted to one follower part. This page implements that principle with a translating yoke and flat faces as an explicit mathematical example.
The drawing is not a reconstruction of a specific packaging machine, loom or valve train. It does not establish an allowable operating speed or a required material, heat treatment, lubrication system or cam-follower size.
Closure calculation for this flat-faced example
Let C be the perpendicular distance between the two follower faces, R1 and R2 the two mean support distances, and c the desired clearance in micrometres. The target return support is R2target = C − R1 − c/1000. The return-size error is R2 − R2target.
The actual signed gap is g = C − R1 − R2 in millimetres. The fourth result is 1000g − c in micrometres: actual gap minus requested clearance. These are geometric results, not pass/fail comparisons against a universal tolerance. A positive g indicates clearance; negative g indicates interference.
For an explicit rotating profile, define support functions h1(phi) = R1 + A cos(2phi) + B cos(phi) and h2(phi) = R2 − A cos(2phi) + B cos(phi), with A = 0.05 min(R1,R2) and B = 0.12 min(R1,R2). A profile point is x = h cos(phi) − h′ sin(phi), y = h sin(phi) + h′ cos(phi).
After cam rotation theta, the upper contact support is h1(pi/2 − theta), while the opposing lower support is h2(−pi/2 − theta). Their sum is exactly R1 + R2 because the sinusoidal terms cancel. The profile curvature radii h + h″ remain positive because R1 and R2 each exceed 3A.
This support-function construction is an illustrative derivation. It is not a general equation for the working radii of arbitrary roller cams. The animation has no RPM input and uses eight seconds per cycle for viewing.
Example: adding a requested 20 micrometre gap
With face spacing C = 100 mm, primary mean support R1 = 42 mm and requested clearance c = 20 micrometres, the target return support is 100 − 42 − 0.020 = 57.980 mm.
If the actual return support remains 58.000 mm, the signed gap is zero. The return support is 0.020 mm larger than the target, so actual gap minus requested clearance is −20 micrometres. The ideal drawing is constrained at zero gap, but it does not provide the requested clearance.
Setting the return support to 57.980 mm gives a 0.020 mm actual gap and zero gap error. Setting it to 58.050 mm instead gives −0.050 mm: an interference condition that the rigid mechanism cannot accommodate.
Interpretation and limits
Positive constraint does not remove the need to consider compliance, inertia, contact loading and manufacturing error. This calculator studies rigid geometry only. A requested clearance is an input to compare, not a universal recommendation.
The cam shapes are convex mathematical examples with a small prescribed motion variation. They are not optimized for acceleration, pressure angle, wear or a particular machine cycle. Contact points migrate along the flat faces as the cams rotate; they are not fixed radial points or rollers.
Choose permissible tolerances and operating conditions using the actual cam geometry, materials, loads and manufacturer information.
Conjugate cam questions
Are the two cam centres separate pivots?
No. The cams share one shaft and are in separate axial planes. Their axial separation is exaggerated in the drawing to expose the profiles.
What does follower face spacing measure?
It is the perpendicular separation of the two opposed flat faces on the rigid translating yoke, not a distance between cam shafts.
Why are there no roller followers?
The four inputs do not include roller radius or offset. Flat faces allow a fully specified support-function example rather than an incomplete roller-profile calculation.
Can a negative gap run?
No. It means rigid parts overlap. The animation is then an interference preview only.
Does zero error prove this design is suitable at high speed?
No. It means the entered geometric gap matches the requested clearance. Dynamic loading, contact stress, stiffness and operating speed are not calculated.
Cam references and model scope
MechDesigner, Conjugate Cam Function Block documentation: multiple cam profiles acting on followers belonging to a single follower part. NPTEL, Drives and Mechanisms, lecture 3: Cams: cam, follower and supporting frame, with motion transferred by contact.
The explicit convex flat-face support functions and closure equations above define this page’s illustrative model. They should not be substituted for the synthesis of a different roller or rocker arrangement.
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