A disk cam moves a translating follower by presenting a changing radius to a guided contact point. The calculator constructs an in-line knife-edge profile from a specified cycloidal lift law. A schematic spring keeps the follower against the rotating surface.
Disk Cam with Translating Follower Interactive Calculator
Generate an in-line knife-edge cam with a cycloidal rise and return. Set lift, base radius, rise angle and shaft speed. The remaining angle completes the return; there are no dwells. The profile and follower stay in contact throughout the illustrated cycle.
Equation Used
- In-line translating point follower, with no lateral offset.
- Cycloidal rise and return, no dwells, and constant shaft speed.
- Positive cam radius and perfect maintained contact.
- Rigid parts; no spring-force, wear, friction or dynamic separation calculation.
- Speed is displayed at 1/100 of the entered rpm so the motion remains visible.
Peaks include both the rise and return. The 30° value is a comparison target, not an approval or machine rating. The visible knife-edge follower is a theoretical point-contact model, not a roller cam or a production-ready profile.
A profile generated from the required motion
The shaft and cam rotate; the follower can only move vertically inside its fixed guide. Its pointed end touches the cam surface. A collar above the guide compresses the illustrated spring as the follower rises.
For each cycle angle θ, the contact radius is Rb+s(θ). The program constructs the cam by placing that radius at local angle 90°−θ. Rotating the completed profile by θ brings the appropriate point back under the follower. The resulting contour gives the guided follower the specified displacement throughout one rotation.
The base circle is dashed. The gold line identifies the current contact normal, while the follower axis gives the direction of translation. Their angle is the pressure angle. The lower trace shows the commanded lift through the complete cycle.
Exploring a motion programme
This calculator compares the geometric consequences of lift, available rotation angle and cam size. It is useful for understanding a reciprocating motion before adding actual follower bearings, loads and contact-force requirements.
The point follower defines the contact geometry used here. A roller has a finite radius and requires a different cam surface to produce the same lift law.
Cycloidal rise and return
Let f(u)=u−sin(2πu)/(2π), where u runs from zero to one during an event. For the rise, s=hf(u); for the return, s=h[1−f(u)]. The rise uses angle β and the return uses 2π−β, both in radians.
The event slope magnitude is h[1−cos(2πu)]/B, where B is that event’s angle. Pressure angle follows tan|α|=|ds/dθ|/(Rb+s). The calculator searches both events for the largest magnitude, using 2,401 samples per event. The return has the same set of displacement-and-slope pairs as a reversed rise with its own event duration.
At constant shaft speed ω, peak speed is 2hω/min(β,2π−β). Peak acceleration magnitude is 2πhω²/min(β,2π−β)². Millimetres per second squared are divided by 1,000 for the displayed m/s².
The 30° target radius is the largest value of |ds/dθ|/tan(30°)−s, with a lower bound of zero. It is a geometric comparison, not a complete sizing rule.
Reading the changing results
Increasing speed multiplies follower velocity linearly and acceleration by the square of speed. It does not change the cam shape or pressure angle, because those are geometric properties.
Increasing base radius reduces pressure angle while retaining the same lift programme. Increasing lift increases the required motion and generally demands a larger cam for the same pressure-angle target.
At a 240° rise, only 120° remains for return. That faster return must be included in the reported peaks. The shorter return event sets the maximum speed and acceleration for this setting.
What the illustration establishes
The generated contour and follower position agree for a complete turn. Cycloidal displacement has zero velocity and acceleration at each event boundary, although jerk changes there. These kinematic properties do not establish acceptable operating forces or speed.
The contact point is idealized, and the spring is only a visual indication of the closing force. Actual roller geometry, contact stress, follower mass, spring preload and stiffness, lubrication and guide strength require separate design work. Large lift with a small base radius can produce a steep pressure angle even though the mathematical profile still closes.
Translating cam questions
Why is there no roller?
The stated model is a knife-edge or point follower. A finite roller requires its own profile offset and curvature checks.
Why does rpm not change pressure angle?
Pressure angle depends on the contour and follower direction. Speed changes velocity and acceleration instead.
Does the return count?
Yes. All displayed peaks cover rise and return.
What does the 30° pressure-angle target mean?
It is a chosen geometric comparison target. Force, contact stress and durability need separate assessment.
Why is the animation slower than the entered rpm?
It plays at one hundredth of shaft speed to keep the contact and motion visible. Numeric kinematics use the entered speed.
Reference
Carnegie Mellon University, Introduction to Mechanisms, Chapter 6: Cams, sections 6.2–6.5: follower constraints, pressure angle, and profile construction by inversion. The cycloidal rise/return programme and equations on this page define the specific mathematical example.
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