Tools:
CAD, FEA, 3D Printing, Motors, MATLAB
Timeline:
3 Weeks
Team:
Genevieve Dandurand, Mathieu Johnson
Project Overview
We designed and fabricated a rack-and-pinion linear actuator supported by a curved beam structure, optimized for strength, manufacturability, and efficiency.
Our mechanism—nicknamed The Very Hungry Caterpillar—converts rotational motor motion into linear motion to deliver high impulse under tight geometric constraints.
Design Concept
The mechanism is driven by a rack and pinion mounted on a curved beam with a varying cross-section.
Rack and Pinion: Selected for direct linear actuation and minimal energy loss due to spur gear efficiency.
Curved Beam: Designed with a varying cross-section to minimize weight while maintaining bending strength.
Idler Gear: Introduced to create clearance for the motor below the platen without affecting force transmission.
Bearing System: Rack constrained by a bearing-supported plate; pinion mounted via steel pin to motor shaft.
Motor and Gear Analysis
We experimentally determined the motor setpoint to maximize power output at V_appl = 1.5 V, yielding 0.86 W.
Key parameters:
Gear ratio: 625:1 (highest ratio compatible with torque requirement)
Transmission ratio: 170 rad/m
Pinion diameter: 0.75” (chosen closest to ideal 0.72”)
Efficiency:
Motor + gearbox (4 stages): 35%
External gears: ~78%
Overall system: 27%
These selections optimized torque transmission and ensured structural integrity while minimizing frictional losses.
Structural Analysis
The supporting curved beam was modeled to assess bending and out-of-plane buckling.
Increased thickness (b) at high-stress regions prevented buckling under pin-pin constraints.
Material removal from the neutral axis reduced unnecessary mass.
Manufactured using Tough 2000 resin for its high ultimate strength (46 MPa vs. 35 MPa for PLA) and low density (1.11 vs. 1.24 g/cm³).
Component Selection
Gears: 0.75” pitch diameter, 14.5° pressure angle, 24-tooth spur gear (maximizing efficiency).
Rack: Nylon material for low weight and sufficient strength.
Bearings: 3 mm needle bearings for compactness and reduced friction.
Shafts: Alloy steel for durability and surface smoothness.
Finite Element Analysis
We performed FEA for three critical loading scenarios, including initial stall torque.
Results:
Minimum Factor of Safety: 1.12 (stall torque condition)
Confirmed structural stability and load-bearing adequacy.
Results & Performance
Mass: 104 g
Total Impulse: 525 Ns
Demonstrated consistent actuation performance and efficient mechanical energy conversion.
