Mechanism 03 of 03

Timing chain drive

Joshua Kyan Aalampour

Every valve opens once per 720°, so the camshafts have to turn at exactly half crank speed. I wanted that ratio to arise naturally from the physical model rather than artificially asserting it.

Both chains running. Each wraps the crank sprocket and one bank's two cam sprockets.

The ratio

I put a 14-tooth sprocket on the crank nose driving 28-tooth sprockets on the cams.

\frac{N_{\text{cam}}}{N_{\text{crank}}} = \frac{28}{14} = 2.000

22 and 44 teeth

I originally used 22 and 44 teeth. The ratio was correct and the animation looked plausible, but the chain never engaged the sprockets (the links never sat down into the tooth gaps, and the chain just passed over them).

Tooth pitch is set by the pitch diameter and the tooth count. But what I had not taken into account is that the pitch is a chord and not an arc, since a chain link is a rigid straight bar and can't follow the curve of the pitch circle. At 22 teeth on that pitch diameter the chord works out to 6.12 mm against the 9.65 mm link, which is 37% short.

p = d_p \sin\!\left(\frac{180°}{N}\right)

Both sprockets are cut on the same 21.5 mm pitch radius, so the tooth count alone sets the chord between adjacent teeth, and that chord is what a rigid link has to span.

Tooth chord is within 0.85% of the link pitch, so the links seat in the gaps and the drive transmits. Matching exactly at this tooth count would want a 43.37 mm pitch diameter against the 43.00 mm as built.

Re-cutting to 14 teeth on the same 43 mm pitch diameter brings the chord to 9.57 mm against the 9.65 mm link, so I went from 37% short to 0.85% short and the teeth and links finally line up. I also swapped the coarse box links for fine rounded roller links, which is both more realistic and necessary for the pitch to work at all.

The remaining 0.85% traces back to the pitch diameter itself. A sprocket cut to match a 9.65 mm chain exactly at 14 teeth wants a pitch diameter of 43.37 mm rather than 43.00, so the as-built sprocket sits 0.37 mm under and the chord falls short by 0.082 mm on every tooth. Across a seven-tooth wrap that accumulates about 0.6 mm (roughly 6% of a link), and on a real drive it would show up as the chain riding slightly high on the last tooth before it leaves the wrap.

One chain, five sprockets

My first routing used a single chain trying to wrap all five sprockets at once (the crank plus all four cams). Laid out around sprockets on both banks, the chain path crossed over itself in the valley between the heads.

Real DOHC V8s generally run one chain per bank, so I rebuilt the drive the same way. Each chain wraps three sprockets (the crank plus that bank's two cams). I generated the path as the convex hull around those three circles, which is what a taut loop physically does anyway. Three circles give a clean triangle with no way for the path to intersect itself.

The first routing and the as-built drive, each loop computed as the outer tangents around its three sprockets, which is the path a taut chain takes.

Dead-on from the front. Each chain closes its own triangle, and nothing crosses the valley.

Chain construction

I built the chain from individual roller link instances placed along the computed chain path rather than as a swept surface or a tube following a curve, each one spaced at the 9.65 mm link pitch, with about 102 of them closing each per-bank loop.

The two chains sit on separate planes along the crank axis, each on its own crank sprocket, the way a production duplex drive stacks its rows. Guide rails and a tensioner run along each loop.

The finished drive

With the drive in place the engine was mechanically complete: one crank angle turning the pistons, both chains, and all four cams at exactly half speed, with every clearance in the assembly verified to zero through the full 720° cycle. I think this is the start of something really damn cool!

Into the valley, through the glass.