In physics class, you can draw a vector and force appears out of nowhere. However, in the real world, force never occurs without a potential field gradient. Mechanical parts require deformation (though often that deformation is very small). Pneumatic actuators use a pressure difference. Electric motors only generate torque when the two magnetic fields (usually winding-generated vs. permanent magnet) are misaligned. Structures class generally covers Young's modulus (E = sigma / epsilon), and statically indeterminate systems but from the perspective of surviving some applied load, not thinking about intentional deformation to create desired forces.
Bearings & Fasteners Need Preload
One immediate insight is that bearings and fasteners need to be preloaded (elastically deformed during assembly) in order to carry load without slop. Without preload, the first bit of applied load to a system will experience no resistance until the system deforms enough to build up a reaction force. Fasteners (0xTBD) and bearings (0xTBD) are each big topics I won't cover here. Simply maintaining a constant preload within a seemingly-static assembly is a major application of springs.
Force for Robot Tasks
The partnership of deformation and force also crucial because many tasks have force goals. As an example, consider a pinch-style gripper (force closure). The upwards force is a function of friction properties and normal force - the precise position isn’t important as long as the force is achieved. By contrast, if this pincher was very rigidly position controlled, a small deformation might greatly change the contact force, resulting in dropping the payload.
Designing in Deflection
If force is a requirement, then deflection is a requirement and you should design that deflection intentionally. Continuing the gripper example, what options are there? What factors need to be considered? Note there's no single right answer - you'll have to do the math on your particular system.