Crank-Slider Mechanism Design & Force Calculator
A crank-slider converts rotation into reciprocating linear motion through a connecting rod. Here x is the slider coordinate measured from the crank center, rather than travel from an end position. The symbol l below is the connecting rod length L in the input panel. For an inline mechanism (e = 0), geometry gives x = r·cosθ + √(l² − r²·sin²θ). For an offset mechanism, replace r²·sin²θ inside the root with (r·sinθ − e)².
When r/l is small and e = 0, expansion of the square root gives x ≈ l + r·cosθ − (r²/2l)·sin²θ. A finite rod length makes the motion depart from a pure sinusoid. At constant angular velocity ω = 2πn/60, velocity is v = ω·dx/dθ and acceleration is a = ω²·d²x/dθ². Use radians when differentiating.
This tool calculates position and velocity from geometry including the offset, but displays acceleration using a ≈ −rω²[cosθ + (r/l)cos2θ]. This is an inline approximation: interpret it cautiously as offset or crank ratio increases. Force is calculated from input torque and the instantaneous moment arm, with a simplified allowance for guide friction based on the friction coefficient.
Crank radius r and rod length L are center-to-center distances in mm. Each input has a minimum of 1 mm, and full rotation requires L > r + |e|. Values of r = 50 mm and L = 150 mm are useful learning inputs. There is no universal absolute length range because machine sizes vary. A smaller r/L favors the approximation above; the tool warns when it exceeds 0.5.
Offset e is the distance between the crank center and slider guide line in mm; the input accepts nonnegative values. Start at zero to study inline motion before increasing it. Speed n is in rpm with an input minimum of 1, and angle θ ranges from 0 to 360°. An actual operating speed range depends on mass, bearings and lubrication; this calculator does not establish that range.
Input torque is in N·m and slider load is an external resistance in N; both accept zero or positive values. The load is used to calculate required input torque. Friction coefficient μ is dimensionless, with an input range of 0–1 and a default of 0.05. Setting μ = 0 provides a frictionless comparison. Select a real coefficient from the contact materials and lubrication conditions.
① Enter r, L and e, then check the full-rotation condition and any warnings.
② Set speed and angle, followed by input torque, external load and friction coefficient.
③ Select Calculate and check the units of position, velocity, acceleration and force.
④ Use the angle slider and animation to examine a revolution. Compare direction changes and force variation on the cycle chart instead of judging peak load from a single angle.
Enter r = 50 mm, L = 150 mm, e = 0 mm, n = 60 rpm, θ = 90°, input torque 10 N·m, load 100 N and μ = 0. Then ω = 2π rad/s and √(150² − 50²) = √20000, giving a position of 141.42 mm. Velocity is −314.16 mm/s, displayed acceleration is approximately +657.97 mm/s², and the inline stroke is 100.00 mm.
At this angle the rod angle is 19.47° and the instantaneous moment arm is 50 mm. Output force is therefore 10000/50 = 200.0 N, and the required torque for the load is 100×50/1000 = 5.000 N·m. Negative velocity means decreasing x. The acceleration value is the output of the approximation above, rather than a claim that it equals exact acceleration.
Links are rigid, pins are ideal connections and crank speed is constant. Force calculations omit mass and inertia forces, shaft flexibility, clearance, impact and bearing losses. Using μ still does not reproduce the speed or temperature dependence of real friction.
Near dead center the moment arm becomes very small, making force calculations sensitive. The tool handles the near-zero case separately; do not interpret the displayed value there as a guaranteed physical force. Stroke is calculated by angle sampling, so offset extrema can carry numerical error. Final design needs dynamics, strength and physical interference checks.
Is stroke always 2r? It is for an inline mechanism. Offset changes the locations of the extrema, so check the calculated full stroke.
Does zero velocity mean zero acceleration? No. Acceleration can remain nonzero at an instant when the slider changes direction.
What changes with a longer rod? With the same r, a smaller r/L makes motion closer to sinusoidal and reduces rod inclination. Consider the resulting machine length and structural requirements as well.