Machine kinematics · Roller envelope

Cam Motion Designer

Turn a real cam profile beneath a guided roller. Design rise, dwell and return, compare cycloidal and quintic motion, and see why a shorter rise makes acceleration and pressure angle grow.

Follower lift $0$

Signed output velocity $0$

Output acceleration $0$

One shaft turn $0$

Signed pressure angle $0$

Peak absolute pressure angle $0$

Minimum normal-offset margin $0$

Contact / linkage residual $0$

Turn & compare

Write motion into the edge.

Shaft phase

\theta

65.00\,{}^\circ

Prescribed shaft rate

\omega

60.00\,{}^\circ/\mathrm s

Base-circle radius

R_b

1.05\,\mathrm m

Follower lift

h

0.45\,\mathrm m

Rise and return angle each

\beta

120.00\,{}^\circ

Roller radius

a

0.15\,\mathrm m

Right and up are positive in the motion plane; depth points toward you. Shaft phase increases counterclockwise from the rightward crank reference. Controls use degrees; internal calculations and CSV use radians, metres and seconds.

The rise begins at the low dwell, followed by a high dwell, a return starting at half a turn, then a low dwell. Rise and return have equal angular duration; each dwell fills the rest of its half-turn. Choose cycloidal or quintic motion with the presets; other controls keep that law.

The pitch curve follows roller centers in the cam frame. The gold profile is its inward normal offset by the roller radius. Signed pressure angle is measured from upward follower motion toward the contact normal, positive when it leans right; only its absolute peak is used for the peak readout. Positive offset margin avoids a local cusp, and is not a strength rating.

Playback runs one phase interval and stops. All curves and exports are exact ideal kinematics sampled over one turn, not acquired measurements. Positions, velocities and accelerations share the same model. Mass, friction, backlash, elastic deformation, real contact loads and drive safety are outside scope.

Contact is maintained by an external ideal constraint; no return spring or preload is simulated. Roller spin is not tracked. Both laws have continuous displacement, velocity and acceleration at dwell joins, but jerk can jump. A smooth picture does not establish separation-free operation.

Ideal planar cam and translating roller, with externally maintained contact and prescribed constant shaft speed. No spring sizing, contact force, friction, roller spin, elastic deformation or separation dynamics.

Start with the essentials

Focus question: Can a follower stop while the cam keeps turning?
One-sentence intuition: A circular dwell segment keeps the follower still. The remaining profile encodes a chosen displacement law.

Core mathematical model

Cycloidal rise

s=h\left(u-\frac{\sin(2\pi u)}{2\pi}\right),\quad u=\theta/\beta

This applies over the rise interval; the return reverses it and the dwells have fixed displacement.

Quintic rise

s=h(10u^3-15u^4+6u^5)

Both laws join a dwell with zero velocity and acceleration; jerk need not be continuous.

Roller-center pitch and true edge

\rho=R_b+a+s,\quad\mathbf p=(\rho\sin\theta,\rho\cos\theta),\quad\mathbf c=\mathbf p-a\mathbf n

The cam frame rotates opposite to the input during construction. The normal is outward from the pitch curve; rotating the edge forward places the contact against the roller.

Pressure angle and offset regularity

\tan\varphi=-\frac{s'}\rho,\quad\kappa=\frac{\rho^2+2(s')^2-\rho s''}{(\rho^2+(s')^2)^{3/2}},\quad m=1-a\kappa

Primes differentiate with respect to shaft radians. The minimum margin readout scans one turn; independent geometric tests check contact and offset regularity across control bounds.

Common difficulties

A kinematic model is not a force model

Typical misconceptionSmooth motion proves the real drive can run at the selected rate.

Better mental modelContact loads, inertia, friction, elastic deformation and drive design need separate models. Parts have schematic thicknesses.

The roller center is not the cam edge

Typical misconceptionThe pitch curve can be manufactured directly as the roller cam.

Better mental modelThe material edge must be offset inward along the pitch normal by the roller radius. A radial subtraction is generally wrong.

Run the experiment

01
Run one turn
Choose the motion-plane view and run or drag the coral crank.
What to observe: The cam keeps turning through each dwell while lift and velocity stay fixed.
02
Make the rise shorter
Keep the lift, shorten the rise angle, then enlarge the base circle.
What to observe: A short rise magnifies speed and acceleration. A larger base reduces pressure angle without changing the lift program.
03
Compare motion laws
Compare cycloidal and quintic presets at the same dimensions, then double shaft rate.
What to observe: Both laws reach the same lift and dwell. Doubling shaft rate doubles velocity and quadruples acceleration.

Geometry & apparatus: CMU · Cams · NITK Virtual Labs · Crank and Slotted Mechanism