| name | enc - Engineering Calculations |
| description | Standard engineering calculation procedures for robotics and mechanical system design — forces, torques, materials, actuator sizing. |
| output | {"format":"prose"} |
Engineering Calculations
Input: $ARGUMENTS
Overview
Structured calculation procedures for mechanical and robotics engineering. Each follows: define requirements, identify relevant physics, select formulas, calculate, verify with safety factors.
Steps
Step 1: Define Requirements
- What must the system do? (load, speed, range of motion, precision)
- Operating conditions (temperature, environment, duty cycle)
- Constraints (size, weight, cost, power budget)
- Safety factor required (typically 2-4x for mechanical, higher for life-safety)
Step 2: Identify Relevant Physics
- Statics: Forces, moments, equilibrium (F=0, M=0)
- Dynamics: Acceleration, inertia (F=ma, T=Iα)
- Strength of materials: Stress, strain, fatigue (σ=F/A, τ=T*r/J)
- Kinematics: Motion, velocity, workspace (DH parameters, Jacobian)
- Thermal: Heat dissipation, thermal expansion
- Electrical: Power, current, efficiency (P=IV, P=Tω)
Step 3: Actuator Sizing (common calculation)
- Calculate required torque: T = F × r + I × α + T_friction
- Calculate required speed: ω = v / r (or from trajectory)
- Select motor: T_motor × gear_ratio ≥ T_required × safety_factor
- Check speed: ω_motor / gear_ratio ≥ ω_required
- Check power: P = T × ω ≤ P_available
- Check thermal: continuous vs peak ratings
Step 4: Structural Analysis (common calculation)
- Free body diagram: identify all forces and reactions
- Calculate internal forces (shear, moment diagrams)
- Calculate stress: σ = M×y/I (bending), τ = V×Q/(I×b) (shear)
- Compare to material yield: σ_max < σ_yield / safety_factor
- Check deflection: δ < δ_allowable
- Check fatigue if cyclic loading
Step 5: Verify
- Units check (every term must have consistent units)
- Order-of-magnitude check (does the answer make physical sense?)
- Boundary check (what happens at extremes?)
- Compare to similar existing systems
CALCULATION SUMMARY:
System: [description]
Requirement: [key spec]
Calculation: [key result with units]
Safety factor: [actual / required]
Status: [passes / fails / marginal]
When to Use
- Sizing actuators, motors, structures
- Mechanical design verification
- Robotics system design
Verification
