Need a geometry genius

I am not a math guy at all. If it weren't for CAD programs I'd never build anything cause I can't calculate an angle to save my life.
In the pic, the right side is the platform arc and the left is the actuator arm arc. The arm is 6" from center to center and the platform is 9" from center to the arm link attachment. 1 motor will handle roll and the other pitch. I've drawn in the numbers but can't determine the best placement for the motor so that the swing of the arm will be as close to directly proportional as possible. I think the connecting rod should be closer to vertical when the platform is at the end of actuator arms travel but I'm not sure exactly how close to vertical. What should be my x and y offset? Can one of you show me the math (or do the math) for me?
Thank you.
John

Hey John, a couple of things. There is a simcalc program here somewhere that will do a lot of the calculations for you and keep your design workable. A search should turn it up.

But an overall comment, on a 2 dof with the pivot under the seat, most use a different arrangement of actuators where roll is push-pull and pitch has both motors working together. That gives you both motors doing the motion in each axis instead of just one.

There is a different design with nested frames that uses one motor on each axis called the Joy Rider. Is that what you are working toward?

Actually, I don’t know that the Joy Rider uses one motor per axis after thinking about it. It may use a similar arrangement as the u-joint pivot kind. But a number of people have built them and details should be in their build threads.

Ah the Joyrider. that was one of the first civilian motion "platforms" that I saw. Made entirely of PVC with a couple of wiper motors driving it. quite the behemoth by today's standards.
I plan on a more compact design. But yes, I plan to have 1 motor for each of the 2 axis. The motors will be nested under the seat. I will primarily be using this for flight simulation so I'm building it with almost 30 degree rotation off of center. I can lower that amount later but I've done enough flying to know that a 60 degree banked turn leans you over pretty good.
I tried using Simcalc. It's a great program but it's set up for a different configuration so it didn't work for me.
The platforms that I've seen here have the push-pull design that you described. I was thinking this is because you could use a less expensive motor as they work in tandem. I scored a couple of pretty beefy motors at the landfill (Yea for free!). That's why I'm planning on using one for each axis.
I'll go take another look and see if anyone is using this type of design. Maybe I can score a math genius in my search...
Thanks.

I think I have it figured out now. Just took turning the motor 90 degrees.