The Evans grasshopper is an approximate straight-line four-bar linkage. The illustrated form uses these link-length ratios: AD=1.41 AB, BC=0.55 AB and CD=0.48 AB, with tracing point E fixed on the rigid coupler triangle by BE=0.45 AB and CE=0.96 AB.
Evans Grasshopper Linkage Interactive Calculator
Run a geometrically closed Evans four-bar, vary its scale and crank sweep, and measure the resulting coupler-point stroke and lateral wander.
Equation Used
- All six bar and coupler-triangle distances remain rigid.
- Planar pin joints and ideal assembly branch.
- Constant cycle rate only sets playback time.
- No force, balancing, bearing, stress, clearance or wear model.
The displayed ratios describe one published Evans four-bar form, not every engine arrangement called a grasshopper. Lateral wander is numerically sampled over the selected sweep; it is not a tolerance guarantee. Strength, dynamics, clearances and wear are outside this model.
A closed four-bar with a coupler point
Frame pivots A and D are fixed. Input link AB turns about A, rigid coupler body BCE connects B to C, and rocker CD closes the chain back to D. Point E is fixed relative to B and C, so its path is determined by the moving links.
The useful portion of E's coupler curve is approximately straight, not mathematically exact.
Historical straight-line guidance
Evans linkages belong to the family of pin-jointed approximate straight-line mechanisms associated with early engines. This diagram explains one published proportion set; it is not a manufacturing drawing for a particular surviving engine.
Circle-intersection kinematics
At every position, B lies on the circle AB about fixed pivot A. Point C is the intersection of circles BC about B and CD about fixed pivot D. Point E is then the intersection of circles BE and CE, fixing it on rigid coupler body BCE.
The calculator samples E across one cycle and reports its vertical range as trace stroke and its horizontal range as lateral wander.
Interpreting the calculated path
Increasing all link dimensions scales both the traced stroke and lateral wander. Increasing crank sweep uses more of the coupler curve and generally increases both. Cycle rate changes only playback timing in this kinematic model.
Scope and limitations
The model preserves all pin-to-pin lengths and shows the actual coupler curve for the entered scale and sweep. It does not calculate forces, pin reactions, bearing clearance, interference, material stress, vibration, lubrication or safe operating speed.
Questions
Is the traced line perfectly straight?
No. This is an approximate straight-line linkage.
Are the links allowed to stretch?
No. The construction solves every moving pin from fixed circle radii.
Does this represent every grasshopper engine?
No. The name covers multiple historical arrangements; this page identifies the exact proportion set used.
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