Two arms rotate about fixed hinge axes while a coupling rod joins their tips. Change the dimensions and primary angle to see whether this four-bar linkage can close and how the follower arm turns.
Linked Hinges Exact Four-Bar Closure Calculator
Vary selected primary angle, follower/primary arm ratio, hinge-center distance and rigid rod length. The solver preserves all pin-center lengths and reports unreachable combinations instead of stretching the rod.
Equation Used
- Links are rigid and planar with ideal revolute joints.
- The solver selects the upper open assembly branch when two intersections exist.
- Leaves, hinge barrels, collisions, forces, clearances and hardware ratings are outside the model.
The arm lengths and coupling-rod length remain fixed. When those lengths cannot meet at the selected angle, the diagram shows a red gap and the calculator reports the closure shortfall.
One closed four-bar chain
Two hinge axes are fixed C apart. The primary arm has stated illustrative length a=C/4, the follower arm has length b=R·a, and a rigid rod L joins their tips. For each primary angle, the follower tip is the intersection of a circle centered on the primary tip with radius L and a circle centered on the follower hinge with radius b.
If those circles do not intersect, the assembly cannot close. The animation shows a red gap rather than changing a link length.
Kinematic feasibility study
The screen can inspect one ideal planar coupling arrangement. Real linked hinges require packaging, collision, leaf stiffness, barrel and pin selection, clearances, stops and load analysis.
Circle-intersection condition
Here d is the current distance from the driven arm tip to the follower hinge. The displayed feasibility margin is the smaller distance to the two equality limits. It is geometry only, not allowable misalignment.
Reading the result
At C=200 mm, R=1, L=200 mm and primary angle 90 degrees, both 50 mm arms and the 200 mm rod close exactly on the selected open branch. Changing L far outside the circle-intersection interval produces a positive closure gap.
Model boundary
No constant angular ratio is assumed. A rigid four-bar generally has a nonlinear follower relationship. The model omits joint clearance, link flexibility, friction, interference, singular load amplification, fasteners and capacity.
Linked-hinge questions
Does R mean an angular ratio?
No. It is explicitly the follower-arm to primary-arm length ratio.
Can the rod stretch to fit?
No. Unreachable inputs show a gap.
Does positive feasibility margin prevent binding?
No. It only proves ideal geometric closure.
Kinematics references
- University of Illinois, Four-Bar Linkages: rigid-link, pin-joint topology and one-degree-of-freedom position relationship.
- Cornell Reuleaux Collection, Four-bar Linkage: historical closed-chain model.
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