This section establishes the analytical sizing and material constraints for the finalized parallelogram linkage arm. The mechanism consists of two identical, parallel tapered circular booms working in tandem to share the vertical camera load while keeping the horizon level.
In a parallel four-bar linkage with pinned joints, the horizontal control arms act as independent cantilevers pinned to a common vertical end platform. When a vertical force $P$ is applied to the camera platform, the load is divided equally between the top and bottom structural booms.
Therefore, each individual tapered tube is sized against a design load of:
$P_{\text{tube}} = \frac{P}{2} = 1.25\text{ lbs}$
To meet the overall static deflection target ($\delta_{\text{target}} = 0.06\text{ in}$) for the combined system, the equivalent bending rigidity ($EI_{\text{equivalent}}$) for each individual tube must satisfy:
$$ \delta_{\text{target}} \ge \frac{P_{\text{tube}} L^3}{3 E I_{\text{equivalent}}} \implies I_{\text{equivalent}} \ge \frac{P L^3}{6 E \delta_{\text{target}}} $$
To identify the optimal material matrix for the structural links, two prominent industrial candidates are evaluated: 6061-T6 Aluminum and Roll-Wrapped High-Modulus Carbon Fiber Composite. The selected material must maximize specific structural stiffness while minimizing total boom weight.
| Material Property | Aluminum 6061-T6 | High-Modulus Carbon Fiber (Longitudinal) |
|---|---|---|
| Young's Modulus ($E$) | $10.0 \times 10^6 \, \text{psi}$ | $\approx 19.5 \times 10^6 \, \text{psi}$ |
| Shear Modulus ($G$) | $3.8 \times 10^6 \, \text{psi}$ | $\approx 4.5 \times 10^6 \, \text{psi}$ |
| Density ($\rho$) | $0.098 \, \text{lbs/in}^3$ | $\approx 0.056 \, \text{lbs/in}^3$ |
Stiffness-to-Weight Optimization: High-modulus carbon fiber delivers a near-doubling of longitudinal elastic modulus ($E$) at roughly 57% of the mass density of aluminum. This exceptionally high specific stiffness allows the design to satisfy aggressive deflection constraints while minimizing the crane's self-weight.
Mass Moment of Inertia Reduction: For a manually operated camera jib, minimizing the mass of the boom links is critical. Reducing the structural mass along the span lowers the crane's total rotational inertia ($I_{\text{rot}} = \int r^2 \, dm$). This directly eases the kinetic effort required from an operator, enabling smooth, fluid starts, stops, and pans without dynamic overshoot or settling oscillations.
Streamlined Assembly and Fabrication: Utilizing an anisotropic metal like aluminum requires extensive custom machining, cutting, and specialized welding of raw stock to achieve complex geometric profiles. Conversely, sourcing pre-fabricated, precision roll-wrapped tapered carbon fiber tubes from specialized composite manufacturers reduces secondary fabrication to near-zero. The structural links are ordered directly to length, requiring only clean pin-joint holes through-drilled at the root and tip boundaries to interface with the pivot brackets.