A bevelled cam rim can drive a bar guided at an angle to its shaft. The historical arrangement is shown here with an illustrative generated rim that produces sinusoidal travel along a fixed 45° guide. Mean rim radius, an equivalent lift angle and speed determine the displayed stroke, amplitude, frequency and lift-to-radius ratio.
Bevelled Disc Cam Interactive Calculator
Set mean rim radius, equivalent lift angle and speed. The generated cam profile follows the oblique rod path while preserving the selected sinusoidal stroke.
Equation Used
- One sinusoidal guide cycle per shaft revolution.
- Fixed 45° oblique guide and ideal point contact.
- Cam rim is generated to follow the selected guide motion.
- Spring maintains contact by assumption; no load or lift-off calculation.
- The numerical A/R output is not a uniform physical face slope.
Explore sinusoidal motion along the oblique guide. The equivalent lift angle sets amplitude relative to mean rim radius; it is not the inclination of a flat cam face.
A cam rim and an oblique bar
Hiscox’s movement 1100 depicts a bevelled disc cam driving a reciprocating bar at an angle to the shaft. The illustration establishes that arrangement but does not specify a dimensional cam profile or a universal stroke equation.
The animation uses a fixed 45° guide and an illustrative generated rim. The prescribed guide travel is s = A cos φ. The rim changes axial position and radius so the ideal tip lies on that same straight guide at every shaft angle. The return spring indicates maintained contact; its force is not solved.
This is a designed sinusoidal example inspired by the historical arrangement, not a recovered manufacturing profile. It is distinct from a flat tilted disk driving an axial follower.
Studying an angled follower path
The model illustrates how a cam profile can accommodate a guide that is not parallel to its shaft. Different prescribed lift curves require different rim profiles. The geometry illustration does not determine a rated speed range or suitability for a particular machine.
Lift and cycle calculations
The calculator uses A = R tan θ and full stroke S = 2A. Here R is mean rim radius and θ is an equivalent lift parameter, defined by tan θ = A/R. It is not a claim that every bevelled cam has that stroke for a physical face angle θ. The A/R percentage is likewise a lift ratio, not a uniform face slope.
For the displayed 45° guide, let β = 45°. At cam coordinate u, the generated rim has axial coordinate x = A cos u cos β and radial coordinate r = R + A cos u sin β. As the cam turns, this rim produces tip travel s = A cos φ along the guide. One revolution gives one complete cycle, so frequency is rpm / 60.
The generated rim remains rigid while rotating. Finite follower size, edge bevel shape, contact stress, spring dynamics and wear are outside this point-contact model.
Worked generated-cam example
With mean radius 30 mm and equivalent lift angle 5°, amplitude is 30 tan 5° = 2.625 mm and full guide stroke is 5.249 mm. At 300 rpm, the rod completes 5 cycles per second. The lift-to-radius ratio is 8.75 percent.
Along the 45° guide, axial and radial excursions are each ±1.856 mm. The rim radius therefore varies about its 30 mm mean. These dimensions belong to this generated example, not to a specified historic cam.
What needs a separate design
The motion prescription provides a geometric illustration, not a manufactured cam design. A usable contact surface, follower shape, return system and structural supports must be developed for actual loads. A sinusoid has no finite dwell; adding a dwell would change the profile.
Bevelled-cam questions
Is θ the physical angle of a flat face?
No. On this generated-rim example it is the equivalent lift parameter atan(A/R). The cam is not a uniformly tilted plane.
Why does the contact radius vary?
The bar is guided obliquely. Its tip changes both axial and radial position as it moves, so the rim must follow both coordinates.
What do the four output values describe?
The radius, angle and speed inputs give full guide stroke, half-stroke amplitude, cycle frequency and the amplitude-to-mean-radius percentage. The percentage describes the chosen lift, not a uniform cam-face slope.
Is this the exact historic profile?
No. The source establishes the oblique-bar arrangement but supplies no exact profile dimensions. The drawing uses an illustrative profile generated from a sinusoidal motion requirement.
Historical reference
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, movement 1100 on printed page 271: bevelled disc cam for reciprocating motion of a bar at an angle to its shaft.
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