I have the following problem: I have an x,y,z reference frame that is to be rotated around its x-axis and around its y-axis. Three axial motors Mp,Mq,Mr (120 deg apart) are responsible for these rotations -- the motors are aligned along the z-axis (they are coming out of the screen -- see picture below). I was told to use the DCM matrices, however I would like to be able to visualize the math that I need to map the x,y rotations to the rotations of the three motor axes.

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In contrast, if I have to displace the frame along its x or y axis, I can use three radial motors Ma,Mb,Mc (the system has a total of 6 motors). I don't have any problems there. I 'see' the math, I simply project the x and y displacements on the three motors (see picture below) and the system behaves as expected ...

enter image description here


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