For an ideal symmetric Sarrus linkage represented by two equal-length folding chains, plate separation is h = 2L sin θ and opposed elbow span is s = 2L cos θ. The top plate remains parallel to the base and translates along the central axis in the constrained model.
Ideal Symmetric Sarrus-Linkage Model
Explore ideal symmetric Sarrus plate separation, opposed elbow span and generalized-coordinate torque.
Equation Used
- All four moving links have equal length L.
- Opposed chains share the same fold angle and ideal revolute hinges.
- The top plate remains parallel and centered above the base.
- Members are rigid; collision, stress, buckling, friction, backlash and tolerances are excluded.
The torque output is not a motor or hinge rating.
Connected spatial constraint
The animation shows parallel base and top plates joined by two opposed folding chains. Every moving link retains length L; paired revolute hinges make the elbows move oppositely while the top plate center stays directly above the base center.
The drawing is normalized and ideal. It omits hinge width, collision, clearances, flexibility and manufacturing tolerances.
What the calculator determines
Select link length, fold angle, axial load and an assumed efficiency. The calculator returns ideal plate separation, opposed elbow span, separation as a percentage of 2L and ideal generalized input torque.
It does not size a motor, hinge, plate or structure and does not predict stress, buckling, friction, backlash, collision or safe load.
Ideal symmetric identities
h = 2L sin θ, s = 2L cos θ and h/(2L) = sin θ. From virtual work for one selected generalized rotation coordinate, τideal = F(dh/dθ)/η = 2FL cos θ/η.
The torque is tied to this ideal coordinate convention. A real actuator or distributed hinge drive requires its actual linkage and load-sharing model.
Selected-input example
For L = 100 mm and θ = 45°, ideal plate separation and opposed elbow span are both about 141.4 mm. With F = 10 N and η = 85%, the selected generalized-coordinate torque is about 1.66 N·m.
Scope and correction boundary
The kinematic identities are retained, while unsupported deployment, aerospace, tolerance, load, material, performance and maintenance claims plus the fabricated CubeSat example and unrelated video are removed.
Real Sarrus design requires full hinge-axis layout, member sections, joint details, collision checks, tolerances and structural analysis.
Questions
Does the top plate rotate?
Not in this ideal symmetric model; it remains parallel and translates axially.
Is fold span a plate dimension?
No. It is the opposed elbow-to-elbow span in the normalized chain geometry.
Can the torque output select an actuator?
No. It is an ideal generalized-coordinate work balance.
Are link stresses checked?
No. Strength, buckling, bearings, friction, tolerances and collision are excluded.
Technical references
- NIST Special Publication 811 — SI units and coherent quantity notation.
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