This revision uses one explicit symmetric endpoint construction. Declared contact-point lift is a chord, the arm remains rigid, and roller-point and output-point arc and chord travel are kept distinct.
Pivoted Follower Chord and Arc Explorer
Enter declared contact-point chord lift, pivot-to-contact radius and pivot-to-output radius. The worksheet solves exact rigid-arm swing plus arc and chord travel; it does not synthesize a cam profile.
Equation Used
- Follower arm is rigid and rotates about one fixed ideal pivot.
- Contact and output point centres remain at declared radii L and R.
- The two endpoints are symmetric about the arm's horizontal centre position.
- Declared lift h is the contact-point chord between those endpoints.
- Animation phase interpolates angular position along the exact circular arc.
- Cam profile, roller radius, pressure angle, force, friction, spring, speed, acceleration, contact stress, wear and lift-off are excluded.
Resolves the page's incompatible lift-angle formulas by defining lift as a symmetric endpoint chord and removes unsupported pressure-angle force, performance, wear and life claims.
A cam can oscillate a roller carried by a swinging arm
US patent 3,946,766 describes cams on a common shaft actuating roller followers carried by oscillating or swinging arms. Other cam-follower patents likewise show a roller maintained in engagement with a cam profile on a pivoted arm.
This worksheet stops at the rigid-arm endpoint geometry. It prescribes the contact-point path and does not claim that a particular rotating cam generates it.
The topology appears in many specialized machines
Patents document pivoted roller followers in loom shedding motions, valve actuation, signaling and machine tools. Each application uses its own cam profile, bearings, closing method and motion law; no generic speed or life rating follows.
Chord lift and arc travel are different quantities
For two symmetric points on a circle of radius L separated by included angle theta, the straight chord is h=2L sin(theta/2), while the circular arc is L theta. Every point on the rigid arm shares theta, so an output radius R has arc R theta and chord 2R sin(theta/2).
A declared chord-lift example
A 10 mm contact-point chord on a 100 mm radius gives 5.73 degrees swing and 10.00 mm contact-point arc. At a 120 mm output radius, the output arc is 12.01 mm and the endpoint chord is exactly 12.00 mm.
This geometry does not synthesize or rate a cam
Cam pressure angle requires an actual pitch curve, follower arrangement and local motion direction. Side force additionally requires contact force. Those inputs are absent, so the former tan(alpha) side-force factor and universal pressure-angle limits are removed.
Unsupported clearances, materials, speeds, branded installations, wear bands, failure cycles, force claims and troubleshooting instructions are also removed.
Pivoted-follower geometry questions
Why not use theta=asin(h/L)?
That expression belongs to a different one-sided vertical-coordinate construction. Here h is explicitly the chord between symmetric endpoints.
Are arc and chord travel equal?
No, though they are close at small angles.
Does this calculate pressure angle?
No. No cam profile is defined.
Does the animation prove contact or safe speed?
No.
Pivoted follower references
- US 3,946,766, Power loom dobby shedding motion: shaft-mounted cams actuating roller followers on oscillating or swinging arms.
- US 2,188,100, Telemetric system: pivoted follower arm with a roller maintained against a cam periphery.
- EP 1,775,432, Roller rocker arm: cam follower carried by a rocker arm about a pivot member.
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