Re: A simple mechanical model of body use.
I'm speaking from my experience studying anatomy, biomechanics, kinesiology, and physical therapy - but the simple act of lifting one's arm is anything but simple. There are a ton of muscles - some we can consciously activate in isolation, others we can't - that have to contract, in sequence, to move the complicated thing we call the shoulder - the glenohumeral joint. And its hard to use plain language to describe this stuff, but I'll try.
If you look up the role of the serratus anterior (boxer's muscle) and the lower fibers of the trapezius in upward scapula rotation and what that means for lifting arms, that might help you visualize "pushing with your triceps" or "scooping the back of your shoulders down to lift the front up." There is way more, of course, to the sequence of events that ultimately lifts the arm, but its a good start. And it gets even more involved if you want to lift the arm while keeping the humerus in a secure, stable position inside the joint (like when you are lifting a heavy load, or when you are trying to transmit force through a punch)
When my taiji partner was teaching me about peng, he kept telling me to pretend I was crushing an egg between my shoulder blades and pushing the resulting mess down into the ground, again with my shoulder blades ("scoop back and down"). My inner PT translated that as "retract and upwardly - yes, upwardly - rotate the scapula" and low and behold my arms went up, elbows first. My deltoids of course were working - but they weren't operating in isolation.