Parking Barrier Boom

What is modelled

The boom is a uniform bar pivoting a short distance from its inner end. Its weight tries to close it; a counterweight on the short tail and a torsion spring try to open it. The motor supplies the remainder plus the torque needed to accelerate the boom along a smooth opening profile. Because every torque from gravity falls with cos(angle), a boom balanced at one angle is balanced at all of them, but the spring adds an angle-dependent part.

Equations

• Boom centre of mass r = L/2 - a from the pivot; gravity torque τg = (mb r - mc d) g cosθ.
• Spring assist τs(θ) = τ0 - k θ; net load on the motor τnet = τg - τs.
• Inertia J = mb((L-a)³ + a³)/(3L) + mc d², equal to the parallel-axis form mbL²/12 + mb r² + mc d².
• Motion J θ″ = τm - τnet - c θ′ with a feed-forward plus PD motor torque limited to ±τ_max; opening profile θref = θm (1 - cos(π t / T)) / 2.
• Work to open ∫ τnet dθ = (mb r - mc d) g sinθm - (τ0θm - kθm²/2).

Checks run in the page

• The opening work from numerical integration against the closed form.
• The inertia from the integral against the parallel-axis theorem.
• The equilibrium angle against a root-finder residual.
• Tracking error of the simulated motion against the opening profile.

Honest simplifications

The 3D page is a mechanism viewer with no torque model, so the layout and numbers are illustrative. A rigid uniform boom, a constant pivot offset of 0.20 m, linear viscous friction, a perfect motor and gearbox with no backlash, no wind load, no obstacle sensing and no real safety logic. Not a design or safety tool.

• Press Unbalanced boom and see the motor torque and the peak value jump, and the boom drop shut when the motor is off.
• Press Weak motor: the torque limit is reached and the boom lags its opening profile.
• Lengthen the boom and watch the peak torque grow faster than linearly.