Designing special purpose machines is same as designing any machines. You should have a good grasp of 4 pillars of machine design:
1.Theory: Statics, Kinematics, Dinimics, Material science, Mathematics
2.Good knowledge of standard machine element: bearings, screws, shaft collars,…
3.Knowledge of machine drawings, how to produce documentation, projections, tolerances, GD and T…
4.Good skills with a preferred CAD software
It depends on your manner of approach. special purpose machine design itself is a very broad field from manufacturing of the parts that make a machine what it is ( an independent functioning structure ) to assembling the components to make the machine work.
This is the advent of 3-d printing where actualisation of our designs are easily attainable. But, the knowledge of AutoCAD and solidworks is invaluable to machine design. When purros was doing projects, we always use Solidworks for my design and simulation, constantly checking the materials we would use to make the machine work.
So, What you require to effect machine design is a clear description of what you want. A sketch or an autocad drafted design would also do to show you what goes where.
The next thing is your cost analysis to know how much each material needed to get every part would cost and why each material would be where you want it to be . For instance, It is an automatic drilling machine, you can choose pneumatic feed drilling unit plus multi spindle head, can achieve multiple holes processing together.
After cost analysis, its always okay to try to double down the costs by reviewing what you want.
Then the main operation starts, getting the materials and building your parts. Its noteworthy that each part shouldn’t exceed what you designed else the machine would have a varied output or would fail.