Gear ratio of the leadscrew

Damping ratio and natural frequency of the relative (elastic) mode

Maximum motor current

Belt pre-tension alone

A_1 = 1, A_2 = 0

A_1 = 0, A_2 = 1

A_1 = 1 / (1+K), A_2 = K / (1+K)​ with K = exp(−ζ ω_n T/2) 

A_1 = A_2 = 0.5 independent of damping

Longer/Delayed effective motion

Shorter rise time

Increased controller bandwidth

Reduced steady-state position accuracy

The impulses become equal in amplitude (A1=A2=0.5) 

The impulses must be separated by a full period

Any impulse spacing works because vibrations self-decay

The second impulse vanishes (A2→0), so the shaper collapses to a single impulse

The shaper is no longer applicable

Smaller time spacing between impulses

Larger time spacing between impulses

The second impulse amplitude decreases

Because they have lower maximum speeds

Because they exhibit higher jerk peaks (steps in acceleration)

Because they have no constant-speed phase

Because they have longer travel times

Minimizes energy consumption without constraints

Maximizes acceleration peaks to shorten time

Time-optimal transfer subject to constraints on velocity, acceleration and jerk

Minimizes vibrations in flexible axes independent of parameters

For approximately time-invariant linear systems

For strongly time-varying or highly nonlinear systems with changing modes

For multi-mode systems with identified parameters

For known, constant natural frequencies

The spacing depends only on stiffness, not on frequency

The spacing equals one full period of the damped natural frequency 

The spacing equals half a period of the damped natural frequency

The spacing is arbitrary

Innsbruck (Austria)

Berlin (Germany)

Munich (Germany)

Vienna (Austria)