A disk cam with an oscillating follower turns shaft rotation into the angular motion of a pivoted arm. This calculator uses an eccentric circular cam and solves contact with a roller on the arm. The animation uses the same geometry as the calculated swing and output-tip arc.
Disk Cam with Oscillating Follower Interactive Calculator
Solve exact roller contact on an eccentric circular disk. Adjust cam radii and arm lengths; inspect valid contact or a clearly marked incompatible-geometry preview.
Equation Used
- Circular eccentric cam profile, not a general rise/dwell cam.
- Fixed 5 mm roller radius.
- Pivot spacing derived from follower length and cam radius.
- Upper assembly branch; return-spring contact assumed.
Specified mounting and 5 mm roller; return contact assumed. Playback slowed 10 times. No dynamic or contact-load rating.
Exact roller contact on an eccentric disk
The cam is a circular disk whose geometric center is offset from its shaft. If the entered minimum and maximum shaft-to-surface radii are Rb and Rm, the disk radius is Rc=(Rb+Rm)/2 and its eccentricity is e=(Rm−Rb)/2. A fixed 5 mm radius roller follows that surface.
The follower pivot is mounted a distance D=√[Lr²+(Rc+5)²] from the camshaft. This is a defined mounting choice for the comparison; it is not an independently entered installation dimension. The arm from pivot to roller has length Lr, while the opposite output arm has length Lo. Both arms rock through the same angle.
A torsion-spring symbol represents the assumed return action maintaining contact. Its force and dynamic adequacy are not calculated. The circular cam has no designed dwell. Equal minimum and maximum radii give a concentric disk with no follower motion.
Using the motion comparison
Compare the geometric effect of radial cam variation, follower length and output arm length. The output tip moves on a circular arc. Increasing the output arm increases its arc distance without increasing the follower angle.
The university reference describes the oscillating roller-follower arrangement and the need to maintain contact. This calculator selects one explicit circular profile; it does not represent every disk-cam motion law.
Circle-intersection solution
The camshaft is O=(0,0), cam center E=e(cosφ,sinφ), and follower pivot P=(D,0). The roller center F must satisfy |F−P|=Lr and |F−E|=Rc+5. The upper intersection of these two circles gives the illustrated assembly. The contact point lies on the line between the disk center and roller center.
Let ρ=Rc+5. A nonsingular full rotation needs D+e<Lr+ρ and D−e>|Lr−ρ|. The entered maximum radius must also be at least the minimum. If these conditions fail, the model keeps a clearly marked geometry preview but does not report a complete working swing.
For a valid cycle, βmax=acos[((ρ−e)²−D²−Lr²)/(2DLr)] and βmin=acos[((ρ+e)²−D²−Lr²)/(2DLr)]. Swing is Δβ=βmax−βmin. Output-tip arc is LoΔβ, with Δβ in radians. Cycle time is 60/n seconds. Cam radial variation is Rm−Rb; it is not itself a follower arc length.
Example with a 50–70 mm cam radius range
With Rb=50 mm, Rm=70 mm, Lr=100 mm and Lo=150 mm, the circular cam radius is 60 mm, eccentricity 10 mm and roller-center contact radius 65 mm. The defined pivot spacing is about 119.27 mm.
The exact angular limits give about 11.5° of swing and 30.1 mm of output-tip arc. Changing Lo changes the tip arc but not the roller contact geometry. At 300 rpm, one cam revolution takes 0.200 seconds. Display playback is slowed by a factor of 10 for inspection.
What the model does not establish
This is a planar kinematic model with a fixed 5 mm roller radius and a stated pivot mounting. It does not calculate spring rate, follower inertia, contact stress, lubrication, bearing life or roller spin. The return spring is assumed to keep contact where the geometry can close.
Invalid circle intersections can show a gap or overlap in the marked preview. The preview preserves the entered arm length and cam outline, making incompatible dimensions visible.
Physical design requires additional checks of contact forces, pressure angle, clearances and operating speed. A longer output arm increases displacement and reduces ideal force for the same torque; it does not multiply angular swing.
Oscillating cam questions
Why does the cam look circular?
Its center is eccentric to the rotating shaft. That offset creates the changing shaft-to-surface radius and drives the follower.
Is output stroke a straight distance?
No. Tip arc is the distance traveled along the circle around the follower pivot.
Why can the full swing become unavailable?
The entered arm and cam dimensions may not admit roller contact throughout a full revolution, or the radius limits may be reversed. The preview remains visible.
Why does speed not change the geometric arc?
This is a kinematic calculation. Speed changes cycle time and playback, while dynamic contact and spring behavior are outside the model.
Follower arrangement reference
Carnegie Mellon University, Introduction to Mechanisms, Chapter 6: Cams, Figure 6-2f and sections 6.2.4–6.2.5. The reference illustrates an oscillating roller follower. This calculator uses the eccentric-circle profile, roller size and mounting equation stated above.
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