A shaped cam converts shaft rotation into a chosen straight-line motion. This example uses a cycloidal rise, an upper dwell, a cycloidal return and a lower dwell. Change the dimensions and timing to see the actual profile, follower travel and pressure angle together.
Cam Producing Variable Rectilinear Motion Interactive Calculator
Adjust stroke, base radius, cam position, rise angle and rpm. The follower, profile and numerical outputs share the current cam angle. Moving a slider pauses playback for inspection.
Equation Used
- Ideal knife-edge follower with zero offset and maintained contact.
- Constant speed: ω=2πN/60 radians per second. Velocity is calculated at the entered actual rpm even though playback is slowed.
- The drawn spring identifies the return constraint; force, deflection, contact stress and loss of contact are not calculated.
- Base radius and stroke share one scale. Guide, shaft and spring dimensions are illustrative.
- Pressure angle is kinematic information, not a load rating or a pass/fail design approval.
The zero-offset knife-edge follower follows a cycloidal rise and return. The current cam angle controls the displacement, contact radius, velocity and pressure-angle readouts. The spring illustrates the intended return action; its force and ability to maintain contact are not calculated.
Guide the load properly. The cam shapes the motion, but the guideway determines whether the follower actually arrives where the profile says it should.
Pressure angle and guide alignment influence the forces and accuracy of a real cam assembly. This calculator shows the ideal geometry; it does not establish acceptable guide clearance or loading.
A cam profile that matches its follower
The disk rotates around a fixed shaft. A guide constrains the follower to vertical travel, and the spring represents the force that would maintain contact during return. The drawing uses an ideal knife-edge tip. Its path is the actual cam surface; adding a roller would require a different profile formed from the envelope of roller positions.
The cyan follower moves with the entered stroke. The orange line shows the normal to the cam surface at contact. Its angle from the vertical follower direction is the pressure angle. The base circle remains fixed in size as the shaped portion turns around it.
Studying prescribed straight-line motion
Rotating cams can program repeatable follower motion in machinery. This demonstrator isolates the geometry and motion law so you can compare stroke, base size, timing and speed. It does not specify a manufacturing profile for a loaded production machine.
Cycloidal rise and return
For a rise of h over β radians, let x=θ/β. Displacement is s=h[x−sin(2πx)/(2π)], and the angular derivative is ds/dθ=(h/β)[1−cos(2πx)]. Multiplying by ω=2πN/60 gives velocity in mm/s when h is in millimetres.
The return starts at 180° and uses h minus the same displacement function, with a negative derivative. Rise and return each use the entered β; remaining portions of each half revolution are dwell.
For this zero-offset knife-edge follower, contact radius is Rb+s. Pressure-angle magnitude is atan(|ds/dθ|/(Rb+s)). Displacement and velocity remain continuous across the dwell boundaries. This kinematic calculation does not establish contact forces or dynamic suitability.
Compare geometry and speed
With a 40 mm stroke, 50 mm base radius and 120° rise, the follower is halfway up its rise at 60°. Displacement is 20 mm and contact radius is 70 mm. At 300 rpm, velocity there is 1200 mm/s. The corresponding pressure angle is about 28.6°.
Double rpm and velocity doubles, while displacement and pressure angle at the same position stay unchanged. Increase base radius and the pressure angle decreases, while the prescribed stroke stays the same. At 180° rise, both dwell intervals disappear.
Geometry is one part of cam design
A larger base radius can reduce pressure angle for the same rise law. A longer rise interval distributes the stroke over more shaft rotation. Speed changes velocity without changing the geometric profile.
Contact maintenance, finite follower geometry, stiffness, materials and loading require additional analysis. The illustrative spring is not sized by this calculator, and no speed is declared suitable merely because the drawing remains in contact.
Questions about the animation
Why is the follower pointed instead of circular?
The equations and profile here describe an ideal knife-edge follower. A finite roller needs an offset envelope rather than the same radial outline.
Why does rpm change velocity but not stroke?
Stroke comes from the profile. Rpm determines how quickly that fixed path is traversed.
What does the orange line represent?
It is the surface normal at contact. The pressure angle is measured between that line and the follower’s vertical direction.
Does the spring prove that the follower will stay in contact?
No. It identifies the intended return constraint; spring force and separation are outside this model.
Construction and terminology reference
Carnegie Mellon University, Introduction to Mechanisms, chapter 6: Cams, especially the knife-edge translating-follower construction, follower constraints and definition of pressure angle. The chosen cycloidal program is stated explicitly in the equations above.
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