A crank carries a pin at a fixed radius from its rotating shaft. In a slider-crank, a connecting rod joins that pin to a guided slider, converting rotation into reciprocation. The rod’s changing angle makes slider displacement differ from a simple sine or cosine curve.
Crank General Interactive Calculator
Change crank radius, rod length, shaft angle and speed. The supported crank drives a pin-jointed rod and a slider constrained to a straight guide. The angle control and travel result follow the live drawing.
Equation Used
- Rigid planar links with pin-center lengths r and L.
- Slider guide passes through the fixed crankshaft center.
- Positive square-root assembly branch for slider position.
- Rod pin-center length remains fixed throughout the motion.
- No load, balance, bearing, collision or allowable-speed calculation.
Rod length is used exactly as entered. When a short rod cannot reach the guide, the diagram shows the gap and the calculator reports that the assembly cannot close.
Crank, rod and guided slider
The shaft rotates in a fixed support. The crank pin follows a circle of radius r, while the other end of the rod remains on the straight guide. Both rod ends are pin joints, so the rod changes angle as the slider moves.
The animation uses the same pin-center dimensions and closure equation as the calculator. The angle slider, cycle scrubber and live travel result refer to the same pose. At zero shaft speed, automatic motion stops while manual inspection remains available.
A rod longer than the crank radius permits this in-line assembly to make a nonsingular full revolution. If the rod cannot reach the guide at a selected angle, a marked gap shows the missing reach.
Rotary and reciprocating motion
Slider-cranks occur in piston machinery and guided reciprocating drives. The slider can also drive the crank, as in a piston engine. The mechanism’s motion does not by itself establish force capacity, cutting performance, pumping output or an acceptable operating speed.
Exact slider position
For crank angle θ measured from the outward guide direction, the crank pin is at (r cosθ, r sinθ). The rod’s horizontal projection is √(L²−r²sin²θ). On the illustrated branch, the slider coordinate is x=r cosθ+√(L²−r²sin²θ).
Travel measured inward from the outer dead center is L+r−x. When L>r, the two dead centers are separated by 2r. The slider travels that stroke twice per revolution, giving mean speed 4rn/60 in mm/s when r is in mm and n is rpm.
At θ = 90 degrees, travel is L+r−√(L²−r²), which is generally greater than r. That is why 90 degrees is not exactly half-stroke for a finite connecting rod.
Example: 50 mm throw and 200 mm rod
A 50 mm crank radius and 200 mm rod give a 100 mm stroke and L/r=4. At 45 degrees, slider travel from the outer dead center is about 17.795 mm. At 60 rpm, the slider’s mean speed over a complete revolution is 200 mm/s.
Changing rod length changes the intermediate positions even though the full stroke remains 2r. Changing speed changes mean speed; it does not change the geometric stroke.
Geometry and operating limits
Short rods create larger rod angles and greater departure from simple harmonic motion. This calculator evaluates position and mean speed, without estimating guide loads, vibration or a permissible rpm.
At L=r the linkage has change-point geometry. For a rod shorter than the crank radius, some crank angles cannot close at all. The calculator identifies change-point geometry and angles where the linkage cannot close. The drawing is a kinematic section; component thickness, collisions and bearing design are not evaluated.
Crank questions
Is throw radius half the stroke?
For the ordinary in-line slider-crank with L>r, yes: full stroke is 2r.
Is the slider motion exactly sinusoidal?
No. The finite connecting rod adds a changing geometric projection. A long rod approaches the simple harmonic approximation.
What does a 170 mm bicycle crank length mean?
It is the radius from the crankshaft axis to the pedal axis, not an 85 mm radius. A bicycle crank alone is not the complete slider-crank linkage shown here.
Why does a red gap appear?
The entered rod cannot meet the guide at that angle. The gap shows how much reach is missing at the selected angle.
Does the mean-speed result give a maximum safe rpm?
No. It gives distance travelled per unit time, without evaluating loads or component limits.
Reference
Yi Zhang, Susan Finger and Stephannie Behrens, Carnegie Mellon University, Introduction to Mechanisms: Planar Linkages, sections 5.2.1 and 5.2.6. The equations here follow directly from the rod-length constraint.
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