Cam Design (`cams`)

Cam Design

Cam profile and motion analysis

Standards catalog

Validation: indicative · Method band: formula

Open calculator

Indicative method: Indicative closed-form or numerical model

Assumptions

Linear elastic material behavior unless noted otherwise.
User is responsible for load combinations and load factors per the selected design code.
Design standard (US/EU/ISO) sets unit defaults and screening check labels — not a full code worksheet.

Limitations

Professional screening / indicative workspace — does not replace a licensed PE or official code compliance review.
Where specialized evaluators are not implemented, checks map solver outputs to catalog templates for orientation only.

Engineering checks

Check	IND	US	EU	ISO
Pressure angle limit	implemented	—	—	—
Cam contact stress	implemented	—	—	—

Purpose

Analyze cam–follower kinematics and kinetics: displacement, velocity, acceleration, pressure angle, and contact stress for a specified cam profile and follower type. Used for motion control mechanism screening in machine design.

Physics & theory

A cam imparts prescribed motion to a follower through shaped surface contact. The displacement curve $s (θ)$ defines follower position vs cam angle. Velocity and acceleration follow $v = d s / d t = ω d s / d θ$ and $a = ω^{2} d^{2} s / d θ^{2}$ . Smooth acceleration profiles (cycloidal, modified trapezoidal) reduce impact and wear compared to sharp velocity corners.

Pressure angle $ϕ$ is the angle between follower motion direction and the normal to the cam profile. High pressure angles increase side thrust on the follower and risk binding. Contact stress between cam and follower uses Hertzian line or point contact depending on follower geometry (flat-faced, roller, or mushroom).

Governing equations

v = ω \frac{d s}{d θ}, a = ω^{2} \frac{d ^{2} s}{d θ ^{2}}

ϕ = arctan (\frac{d s / d θ}{r + s + s _{offset}})

σ_{c} = \frac{F E ^{*}}{π b ρ _{eq}}

Numerical method

Kinematic differentiation of user-defined or standard motion laws (constant velocity, SHM, cycloidal). Pressure angle computed at each cam angle step. Contact force from follower mass, spring force, and inertia $F = ma + k s + F_{ext}$ . Hertzian contact stress screened against material allowable.

Inputs

Parameter	Description
Cam base radius, motion law	Profile geometry
Follower type	Flat, roller, or oscillating arm
`speed`	Cam angular velocity
Follower mass, spring rate	Dynamic force
Lift, dwell angles	Motion program

Outputs

Displacement, velocity, acceleration plots
max pressure angle
contact force
contact stress
torque required.

Design codes & checks

Indicative: Pressure angle limit, cam contact stress screening

Assumptions & limitations

2D planar cam; no 3D spatial cams or conjugate surface optimization.
Rigid cam and follower; no compliance or lubrication film analysis.
Single-dwell motion programs; multi-segment profiles user-defined.
Manufacturing eccentricity and wear not modeled.

References

Shigley, J. E., & Budynas, R. G. Mechanical Engineering Design, 11th ed., Ch. 16.
Norton, R. L. Design of Machinery, 6th ed. McGraw-Hill.
Chen, F. Y. Mechanics and Design of Cam Mechanisms. Pergamon.
Hertz, H. On the Contact of Elastic Solids (contact stress foundation).
PhyCalcPro verification benchmarks in src/data/verification/ where available for this module.
Beer, F. P., et al. Mechanics of Materials, 8th ed. McGraw-Hill — foundational stress and deformation theory.

Maintainer note: Kinematic profile logic can evolve into richer optimization.

Cam Design

Assumptions

Limitations

Engineering checks

Cam Design (cams)

Cam Design (`cams`)