Gooch valve gear uses two eccentrics to move a curved expansion link, with a radius rod carrying the link block and driving the valve. The reversing control raises or lowers the radius rod while the link’s suspension remains at its set position. “Stationary link” describes that reversing arrangement: the link still swings and moves during every shaft revolution.
Gooch Valve Gear Interactive Calculator
Change the radius-rod lift setting and follow the connected rods through a full turn. The calculator gives valve displacement, total travel and clearance beyond equal outside lap for the illustrative geometry below. Result tiles use the selected crank angle; the animation continues from it.
Equation Used
e is eccentric throw in mm. At e=12 mm, the shaft is at (−220,0), fixed suspension pivot N at (0,−150), and nominal link midpoint at (0,0). The curved slot and radius rod both have radius/length R=200 mm; the slot extends ±20 degrees. The two eccentric phases are crank angle ±120 degrees. Equal eccentric rods are L=√([220+R(1−cos20°)]²+[R sin20°]²). The suspension length h is 150 mm. A 100 mm lifting hanger connects H=(100,−100+22s) to radius-rod midpoint K, where s is the lift setting divided by 100. All lengths scale with e/12, apart from the independently entered lap. Coordinates use downward-positive y. The valve axis is horizontal. Travel is sampled at 720 shaft positions. Lift setting is not cut-off percentage, and lap clearance is not flow area. Display speed is one fifth of entered rpm.
A moving link with a fixed reversing suspension
The two eccentric centres turn around the shaft. Their rods connect to opposite ends of the expansion link. A suspension arm joins the link’s midpoint to a fixed frame pivot, so the rods and arm constrain the link to a repeating combination of translation and rotation.
The radius rod runs from die block D in the curved slot to the horizontally guided valve end V. A lifting hanger acts on the middle of the radius rod. Changing its upper support position shifts the block’s working region within the link, selecting a different combination of the two eccentric motions.
During a revolution the block can slide slightly in the slot while all the connecting rods keep their lengths. The animation includes that motion. It does not pin the block to a chosen material point on the link.
Calculate positions from the rod constraints
The eccentric centres are known from crank angle and throw. The two equal eccentric rods and the link suspension determine the link’s position and orientation. The block is then located on its circular slot so that the radius rod reaches the valve axis and the lifting hanger retains its length.
Valve displacement is measured from the stated nominal valve position. Full travel is the difference between the largest and smallest valve positions sampled over one complete revolution. The two lap-clearance results are the positive distances by which the valve edge has passed the entered outside lap.
The controls scale an illustrative assembly. The geometry has finite rods and a swinging suspension; it is not a valve-setting drawing for a particular locomotive. Piston position, steam-port width and admission events are not included, so the calculator does not report piston-stroke cut-off.
Compare lift, lap and speed
Start with 12 mm throw and a 70% lift setting. Pause the animation and sweep the crank-angle control to follow the selected valve displacement. Move the lift setting through zero to −70% and compare the resulting cycle.
The lift percentage describes the hanger adjustment in this model. It does not mean 70% steam admission or 70% valve travel. Near the central setting the link and eccentric rods still move, and the valve can retain some motion.
Changing lap affects edge clearance without changing the rods or their travel. Doubling throw doubles all model dimensions and valve travel. Changing rpm alters the animation rate only; at zero rpm the angle control still lets you inspect the assembly.
Gooch and other link motions
Historical engineering texts describe Gooch’s arrangement as a fixed-link alternative to Stephenson’s shifting-link motion. Gooch shifts the radius rod to change gear; Stephenson shifts the expansion link relative to the valve connection. Allan’s arrangement combines link and radius-rod shifting.
The Gooch link is curved to suit the radius rod, with its concave side towards the valve. Its constant-lead characteristic is associated with that geometry in the classical valve-motion analysis. Finite rod lengths, suspension placement and the complete valve arrangement still matter when calculating a particular engine’s events.
What this motion drawing helps explain
The two eccentric rods provide different components of motion, and the curved link lets the radius rod select between them. Keeping the reversing adjustment out of the link suspension changes the way the mechanism must be supported and controlled.
The model shows rigid rods, a circular slot and ideal pin joints. Crossing rods occupy separate axial layers. It does not specify machining clearances, material hardness, wear life, steam consumption or operating settings for an engine. Those values require its actual drawings, valve dimensions and load conditions.
Frequently asked questions
Does the stationary link stay motionless?
No. Its suspension is not raised and lowered for reversing, but the eccentrics still make the link oscillate during running.
Which part does the reversing control move?
It raises or lowers the radius rod through a lifting linkage, changing where its die block works in the curved expansion link.
Is the lift-setting percentage the cut-off percentage?
No. It is the selected hanger adjustment in this example. Piston-stroke cut-off requires the complete piston and valve-event geometry.
Why does the block slide during a revolution?
The radius rod, valve guide and lifting hanger constrain its position while the curved link moves. The block must slide to satisfy those connections.
Why is there motion at the central setting?
The eccentric motions do not generally cancel every component of valve movement. The finite linkage shown retains motion near its central setting.
Does this calculator establish exact constant lead?
No. Constant lead is a characteristic of the classical Gooch arrangement, but this finite illustrative assembly does not model the complete piston, valve centring and port events needed to verify an engine’s lead.
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