Motorized Monitor Stand

I have a corner bench I often work at that's impractically large to turn into a full standing desk. I still wanted the benefits of one, though — so the obvious solution was to build a custom, motorized monitor stand. It carries dual monitors and supports homing, jogging, and two saved positions for sitting and standing.

I did the full mechanical design in Onshape (view the CAD here) and machined all of the custom parts myself.

Travel

650 mm

Payload

~40 lb

Drive

TR8×2 lead screw

Motor

NEMA 24 stepper

Sizing the motor

To pick the motor, I sized the lead-screw drive — working out the torque needed to raise the load and checking that the trapezoidal screw won't back-drive (so the stand holds its position). The total torque splits into the torque to hold and raise the load and the torque to accelerate the system:

$$T = T_\text{load} + T_\text{acceleration}$$

Load torque

The drive uses a TR8x2 single-start trapezoidal lead screw:

Parameter	Symbol	Value
Pitch / lead	$l$	2 mm
Outer diameter	$D$	8 mm
Mean diameter	$d_m$	7 mm
Half flank angle	$\lambda$	$15^\circ$

The screw is stainless steel running in a bronze nut, which gives a typical greased friction coefficient of $\mu = 0.1$. From the geometry:

$$\tan\alpha = \frac{l}{\pi d_m} = \frac{2}{7\pi} = 0.0910 \;\Rightarrow\; \alpha = 5.2^\circ$$

The half flank angle inflates the friction into a virtual friction coefficient and angle:

$$\mu' = \frac{\mu}{\cos\lambda} = \frac{0.1}{\cos 15^\circ} = 0.1035 \qquad \tan\phi = \mu' \;\Rightarrow\; \phi = 5.91^\circ$$

which sets the drive efficiency:

$$\eta = \frac{\tan\alpha}{\tan(\alpha + \phi)} = \frac{\tan 5.2^\circ}{\tan 11.11^\circ} = 0.463$$

Estimating the two monitors, arms, and carriage at ~40 lb ($178\,\text{N}$), the torque to raise the load is:

$$T_\text{load} = \frac{F d_m}{2}\tan(\alpha + \phi) = \frac{178\,\text{N}\,(0.007\,\text{m})}{2}\tan 11.11^\circ = 0.122\,\text{N·m}$$

Will it back-drive?

A screw holds its position (won't back-drive under load) when the lead angle is smaller than the friction angle, $\alpha < \phi$. Here $5.2^\circ < 5.91^\circ$, so the stand stays put with the motor unpowered — no brake needed.

Acceleration torque

The rest of the torque accelerates the system, $T = I\alpha$ (here $\alpha$ is angular acceleration, not the lead angle above). Sizing the motion for the full travel:

Quantity	Symbol	Value
Total travel	—	650 mm
Full-travel time	$t$	60 s
Linear speed	$s$	~11 mm/s
Rotational speed	$\omega$	5.5 rev/s = $34.56\,\text{rad/s}$
Time to full speed	$t'$	2 s
Target acceleration	$\alpha$	$\omega / t' = 17.28\,\text{rad/s}^2$

The inertia is the lead screw's rotational inertia plus the reflected inertia of the linearly moving payload:

$$I_\text{screw} = \frac{1}{2}m_\text{screw}\left(\frac{d_m}{2}\right)^2 = \frac{1}{2}(0.213)\left(\frac{0.007}{2}\right)^2 = 1.30\times10^{-6}\,\text{kg·m}^2$$ $$I_\text{payload} = m_\text{payload}\left(\frac{l}{2\pi}\right)^2 = 18.2\left(\frac{0.002}{2\pi}\right)^2 = 1.84\times10^{-6}\,\text{kg·m}^2$$ $$I_\text{total} = I_\text{payload} + I_\text{screw} = 3.14\times10^{-6}\,\text{kg·m}^2$$ $$T_\text{acceleration} = I_\text{total}\,\alpha = (3.14\times10^{-6})(17.28) = 5.4\times10^{-5}\,\text{N·m}$$

That acceleration torque is negligible — about four orders of magnitude below the load torque — and that makes physical sense. The lead screw's 2 mm lead is a huge reduction from rotation to translation, so the payload's mass reflects back to the screw through a $(l/2\pi)^2$ factor of order $10^{-7}$. Eighteen kilograms of monitors ends up "feeling" like less than $2\times10^{-6}\,\text{kg·m}^2$ of rotational inertia, so almost all of the motor's job is simply holding the load against gravity, not accelerating it. The total requirement stays essentially $T \approx 0.122\,\text{N·m}$.

The stand is controlled by an Arduino, which takes inputs from a 5-button controller and the limit switches. It's driven by a NEMA 24 stepper motor through a DM556 stepper driver. You can find the code on my GitHub here.