Thread: [SOLVED] Direction of travel for a wheel oriented at a compound angle

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