Read the result
The angle sets the geometry. Angular speed converts derivatives with respect to theta into time rates.
Rates of change
Crank-Piston Differentiation Simulator
Turn crank geometry into displacement, velocity, and acceleration values.
Formula
x(theta)=r(1-cos(theta)+m-sqrt(m^2-sin^2(theta)))
Result
Worked substitution
Differentiation turns the displacement relation into velocity and acceleration once angular speed is known.
Where it helps
Useful for seeing why differentiation matters in mechanism motion.
Common slip
Degrees are used for the input angle, but the calculation converts internally to radians.
Try it
Try theta = 0, 90, and 180 degrees and watch where velocity is largest.