A grooved cylinder cam moves a guided follower along the cylinder axis as the cam rotates. The groove defines the displacement at each angle. This calculator examines a constant-slope rise: choose diameter, lift, rise angle, speed and output force to compare pressure angle, average rise speed and ideal force and torque.
Grooved Cylinder Cam Interactive Calculator
Vary drum diameter, lift, rise angle, speed, and load to see pressure angle, travel speed, drive torque, and follower side load.
Equation Used
The rise is treated as a constant-slope ramp on an unwrapped cylinder. Diameter and rise angle determine slope; output force determines the ideal transverse force and torque. The calculation has no friction or inertia term and does not establish a load rating.
- Rise is approximated as a constant-pitch helical groove over the selected rise angle.
- Friction, roller inertia, groove clearance, and detailed cycloidal acceleration are ignored.
- An acceptable pressure angle depends on the actual follower, guide, load and motion profile; no universal limit is applied here.
Pressure angle relates the contact direction to the follower’s motion. Its value helps resolve force components, but does not by itself establish bearing life or a permissible operating load.
For a fixed lift and rise angle, increasing diameter reduces the ideal transverse force, while the larger radius keeps the ideal input torque unchanged.
How the groove determines follower position
The cam rotates while a guide constrains the follower carriage along its axis. Contact with the groove flanks drives the carriage outward and back. The groove may include rise, dwell and return portions, each defining a different relationship between shaft angle and axial position.
The cylindrical view wraps the follower-center path around the rotating drum. The gold roller stays on a fixed guide while the groove moves past it. A constant-slope rise forms a helical segment. Roller diameter and groove width are illustrative, not machining dimensions.
Main components
- Cam cylinder: rotates with the input drive.
- Groove: defines the follower-center path and provides opposing contact flanks.
- Follower and carriage: transmit the output load.
- Guide and supports: constrain the required motion and carry reaction forces.
Positive return does not remove clearance or elastic deflection. A physical groove also needs compatible roller size, wall geometry, transitions and lubrication.
Planning a shaft-synchronized motion
A grooved cylinder cam can sequence a transfer carriage, guide or tool slide in relation to a rotating shaft. It is useful when the displacement pattern repeats mechanically and the relationship to shaft angle matters.
This tool compares a single rising segment. A whole-machine design also needs the return, any dwells, the drive ratio and the load throughout the cycle. A rotating output or indexing turret requires its own geometry; it is not established by the translating-follower model here.
Ideal constant-slope rise
q = L/c
α = atan(q)
v = 6LN/β
Ftransverse = Fq
T = F(D/2000)q
D is groove-center diameter in mm, L is lift in mm, β is rise angle in degrees, N is shaft speed in rpm and F is axial output force in newtons. The developed circumferential distance c is in mm, q is dimensionless, v is average rise speed in mm/s, and T is ideal torque in N·m. D/2000 converts the radius from millimetres to metres.
Under ideal frictionless, quasi-static contact, the axial load and groove slope determine the transverse force. Total normal contact force would be F/cos(α); the displayed Side Load is only its transverse component. The calculation does not include follower mass, friction, bearing losses, deformation or contact stress.
For a general smooth groove, velocity is v = (dh/dθ)ω, using θ in radians and ω in rad/s. Here the slope is constant during the rise. Its sharp junctions with other segments are not a physical acceleration profile; smoothing them would change instantaneous velocity and force.
Example: a 30 mm rise over 120°
Enter diameter 80 mm, axial travel 30 mm, rise angle 120°, speed 300 rpm and output force 200 N.
- Developed rise distance: π × 80 × 120/360 ≈ 83.7758 mm.
- Slope: 30/83.7758 ≈ 0.358099.
- Pressure angle: atan(0.358099) ≈ 19.70°.
- Rise duration: (120/360) × (60/300) ≈ 0.066667 s.
- Average rise speed: 30/0.066667 = 450 mm/s.
- Transverse force: 200 × 0.358099 ≈ 71.62 N.
- Ideal torque: 200 × 0.04 × 0.358099 ≈ 2.865 N·m.
Doubling speed doubles average rise speed but leaves these quasi-static force outputs unchanged. Doubling diameter halves slope and transverse force, while ideal torque stays at about 2.865 N·m. These results do not include any acceleration load at the segment boundaries.
How each input affects the comparison
| Change, with other inputs fixed | Ideal model response |
|---|---|
| Increase diameter | Lower pressure angle and transverse force; unchanged ideal torque and rise speed. |
| Increase lift | Greater slope, rise speed, transverse force and ideal torque. |
| Increase rise angle | More time and circumference for the same lift, reducing slope and speed. |
| Increase shaft rpm | Greater rise speed; no change to the quasi-static force calculation. |
| Increase axial force | Proportionally greater transverse force and ideal torque. |
Details the calculation does not resolve
Contact stress depends on the roller and groove geometry, materials and load distribution. Clearance and deflection affect positional accuracy. Lubrication and bearing conditions affect friction and wear. None of these quantities can be inferred from pressure angle alone.
Wear, noise or heat can have several causes. The displayed ideal values cannot diagnose a particular machine or prescribe a replacement fit.
From a rise calculation to a complete cam
Specify the entire displacement curve, including return and dwells. Check continuity of displacement, velocity and acceleration at each join. Then include moving mass and applied load through the cycle, resolve guide and contact forces, and check the chosen bearings and groove geometry against their requirements.
The drawing’s straight return is included only to show a repeating path. It is not a recommended return law, and its forces are not included in the outputs. The eight-second playback is for inspection; it is not real-time motion at the entered rpm.
Frequently asked questions
Why does increasing Speed leave Drive Torque unchanged?
The torque calculation is quasi-static and frictionless. Speed changes the rise time and average speed; follower inertia and other speed-dependent loads are not included.
Why does increasing diameter leave ideal torque unchanged?
For fixed lift and rise angle, the larger radius is offset by the smaller groove slope. The required ideal work per unit shaft rotation stays the same.
Is Side Load the complete contact force?
No. It is the transverse component F tan(alpha). In the ideal model the normal contact force would be F/cos(alpha).
Does the pressure angle apply throughout the animation?
No. It describes the constant-slope rise only. The return is illustrative and may have a different slope.
Can I use the displayed curve as a manufacturing profile?
No. It shows a follower-center path without roller diameter, groove width or wall offsets. The sharp segment joins also need a suitable motion law.
Is 30° always an acceptable pressure angle?
No universal limit is established here. The follower arrangement, guide stiffness, contact geometry, loads and dynamics must be checked.
Is the playback speed the entered rpm?
No. Playback takes eight seconds per illustrated cycle. The entered rpm is used in the numerical average rise speed.
What information is missing for acceleration?
A smooth displacement law through the transitions, along with the complete cycle. The displayed constant-slope rise and straight return have abrupt velocity changes at their joins.
References & Further Reading
- Wikipedia contributors. Cam. Wikipedia
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