I am designing a drive train for a robotics project. There are to

be three wheels- two in front and one in back. The back wheel is

fixed. The front wheels are both attached to arms that have two

rotational axes (Shoulder Joints). The shoulder joint rotates about

one axis that is parallel to the axis of the rear wheel (X) and one

which is perpendicular to the rear axis(Z). The wheel is attached

at the end of the arm and it rotates about an axis perpendicular to

the X and Z axes (Y). I need help figuring out the direction of

travel for a wheel at given angles of rotation for both X and Z

axes. The X axis has 180 degrees of total movement and the Z has 90

degrees of movement obviously the wheel can rotate a full 360.

The way that I plan to turn the robot is by rotating one arm's X axis

forward 90 degrees and having it's Z axis at -45 degrees from

horizontal. The other arm's X axis is rotated backward 90 degrees

and it's Z axis at -45 degrees to horizontal. This causes the robot

to lean into a wide sweeping turn. I need to figure out how to

model this behaviour so that I can send the appropriate data to the

servos controlling the joints.

I have attached two pictures. One is the arm itself, and the other is of the entire robot layout. These are just rough models, meant to illustrate the axes of movement. The second picture shows that the rear wheel also has a shoulder joint disregard this as I plan to leave it fixed as mentioned above.

Any help would be greatly appreciated