How can I assemble multiple stl files in a particular fashion (CAD assembly)?

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I've got a testbed that can import the individual STL files. I have 3 STL files that combine to form a particular assembly. Using Homogenous transformation matrices, I plan to calculate the exact translations/rotations needed for the three parts to assemble correctly. I'm not quite sure how to go about loading & combining the three STL files.

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