Stiff machines are also fast machines
Why rigidity sets the speed at which a machine can be driven.
A stiff machine can be driven faster because stiffness raises the frequency at which its structure naturally wants to vibrate. Any attempt to move a machine faster than its structure can settle excites that vibration instead of producing the crisp motion intended, so the achievable speed of a real machine is set as much by its rigidity as by the power driving it.
A fishing rod whipped back and forth
Wag the tip of a long, floppy fishing rod quickly and it lags visibly behind the hand, then keeps whipping for a moment after the hand has stopped, because the rod stores the energy of each change of direction in its flex and releases it slowly as wobble. A short, stiff rod put through the same motion tracks the hand closely and settles almost the instant the hand stops. Choking up on the floppy rod, gripping it closer to where the flex begins, makes the same wag crisper without changing the rod at all, because a shorter free length is a stiffer one. A machine's structure faces the rod's dilemma every time it is commanded to move quickly.
Stiffness, mass and the speed ceiling
Every structure has a natural frequency at which it prefers to vibrate, set by its stiffness relative to the mass it carries: stiffer means higher, heavier means lower. Trimming mass without preserving stiffness can therefore lower a mechanism's speed ceiling even when the redesign looks like an improvement on paper. A control system moving a mechanism quickly is asking its structure to respond and settle within a time comparable to its own vibration period, and pushing the demand close to the structure's resonant frequency produces overshoot, ringing and a settling time often longer than a gentler command would have needed. A slightly slower move that avoids exciting the resonance can finish and settle sooner than a faster one that spends its apparent advantage on vibration it then has to wait out.
This ties stiffness to the control loops covered elsewhere in this era. A controller's achievable speed of response, its bandwidth, is capped by how quickly the physical structure can follow, and no tuning inside the controller can make the real system settle faster than the structure allows.
Why a bigger motor makes it worse
Fitting more power or a faster motor to a mechanism limited by its structure excites the same vibration harder, since the natural frequency, the real ceiling, has not moved. Diagnosing this means watching how the mechanism settles as well as timing how quickly it arrives. A structure fighting its resonance overshoots its target and oscillates visibly before coming to rest, and a stronger motor reaches that overshoot sooner without shortening the ringing that follows.
Stiffness is therefore a speed specification in its own right. Where more speed is needed, stiffening the structure is often the change that delivers it, using the tools covered earlier in this era: a stiffer material, a shorter unsupported length, a rib or a brace. A mechanism that only ever moves slowly relative to its natural frequency gains little from further stiffening, and the added material, weight or complexity would buy speed the application never asked for. The aim is to match stiffness to the speed required. The final article in this set turns to the danger a natural frequency creates even when nobody is asking the structure to move quickly.