ok, ive got 2 shafts which i need to install to run linkages dor 2 opposite banks of throttle bodies. the linkages need to pull towards the centre.
the shafts (onto which the linkages are fitted) need to rotate in unison (in opposite directions of rotation). they need to be linked precisely, and have the same amount, and rate of rotation relative to each other. not good if the banks of throttle open differently, ezpecially at low degrees...
the shafts are 10mm dia, and can have a separation of 100mm to 25mm
the easiest and most obvious way to make this work is with 2 meshed gears on each shaft. problem is, said gears cost $97 each. plus it looks ugly.
the alternative is to use a linkage mounted between a crank on each shaft. i happen to have some cranks that will fit the shafts, the length of the cranks are 30mm.
the question is, given that crank length, what should the sepration of the shafts be, and what should be the origin angle of each crank on each shaft (and obviously, what is the resultant lenth of the joining linkage).
this is obviously tough as due to bloody trigonometry, and the changing relative angles of the cranks and linkage through 90deg rotation, the ratio of angular movement between the shafts isnt quite 1:1 at all positions.
so far i have mocked up a few examples, and the best i can find so far is to have a separation of 67.5mm, a linkage length of 48mm, and radial origina of the cranks of 0deg and 90deg respectively. this seems to give the closest output of 1:1 mmovement, though there is a bit of wandering. obviously fidelity is most important around the first 20odd deg for smooth off idle throttle control...
the image below describes this 67.5mm separation. (this is the best ive com up with so far). the movement is referenced from the left shaft. as you can see, there is some tiny lag in the right shaft in the first few deg, which soon catches up, and overtakes, only to come back to nearly 1:1 at WOT importantly, see around 10-20deg, the movment is very 1:1

this following image is at 65mm separation (only 2.5mm difference) yet you can see that this has a big effect on the ratio of movement. specifically look how far ahead the right shaft gets even at only 20-30deg...

so, the question is!! can anyone come up with a BETTER way to link these shafts to provide as close to 1:1 motion over the full 90deg?? is there an equation that we can solve to determine the correct separation of the shafts, and the angular origins of the cranks to achieve this goal?
i have just been trial and erroring the diagrams and obsercing the effects changes to these dimensions has - however, there must be a mathematical way to describe this to yeild an optimal solution??
if not, does anyone have any other bright ideas as to how to link the movement of these two shafts???
perhaps a solution is to not have the cranks travel through 90deg at all, and simply change the ratio of the linkages to the throttles so that this 90deg shaft rotation isnt required ro achieve 90deg rotation of the throttle plate? (which is a pita as all my other cranks and linkages are designed for 90deg rotation!)
and before anyone says im mad for trying this, i got the idea from the toyota f1 linkage design:

so yeah, any thoughts!!
cheers
ed

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