For an ideal Scotch yoke with crank radius r and angle θ measured from the positive slider axis, displacement is x = r cos θ, stroke is 2r, velocity is −rω sin θ and acceleration is −rω² cos θ.
Ideal Scotch-Yoke Kinematics
Explore ideal Scotch-yoke position, stroke, velocity and acceleration at a selected crank angle.
Equation Used
- Crank radius is fixed and the pin remains captured in a vertical slot.
- The yoke translates only along a horizontal guide.
- Angular speed is constant.
- Clearance, friction, compliance, loads and stress are excluded.
Animation interpolates to the selected endpoint; output tiles report that selected angle.
Rigid crank and constrained slot
The animation shows a crank pin at fixed radius, captured by a vertical slot in a yoke constrained to translate horizontally. At every pose, the pin and yoke center share the same x-coordinate.
The presentation interpolates from zero to the selected angle; the numeric outputs describe the selected endpoint.
What the calculator determines
Select crank radius, crank angle and constant speed. The calculator returns ideal displacement from mid-stroke, total stroke, instantaneous velocity and instantaneous acceleration.
It does not calculate force, torque, side load, contact stress, clearance, friction, wear or safe speed.
Ideal harmonic identities
ω = 2πn/60, x = r cos θ, stroke = 2r, v = −rω sin θ and a = −rω² cos θ. Acceleration is converted from mm/s² to m/s².
Selected-input example
For r = 50 mm, θ = 0° and n = 60 rpm, x = 50 mm, stroke = 100 mm, velocity is zero and acceleration is about −1.97 m/s².
Scope and design boundary
The ideal motion is sinusoidal and has no connecting rod. Real design requires pin/slot clearance, lubrication, contact pressure, yoke guidance, balancing, loads, fatigue and guarding.
Unsupported application, material, tolerance, maintenance and failure claims are removed.
Questions
Where is x = 0?
At mid-stroke, when θ is 90° or 270°.
Why is stroke 2r?
The slider ranges from +r to −r.
Does speed change position?
Not at a specified angle; it changes velocity and acceleration.
Can this size the pin or slot?
No.
References & Further Reading
- Wikipedia contributors. Scotch yoke. Wikipedia
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