U-Chain Dashboard

U-Chain Geometry Component
\( W_{\text{int, channel}} \) Internal Channel Width (m) 0.000000
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Purpose: Inner Core Sleeve.
Logic: The interior width clearance of the U-channel cap required to perfectly envelope the structural gear face.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Predicted Gear Width (m)
Python Logic: N/A
Live Evaluation: N/A
\( X_{\text{sidewall, running}} \) Sidewall Running Clearance (m)
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Purpose: Thermal Air Gap.
Logic: An operational clearance tolerance on either side to prevent friction-wear against the spinning wheel.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
Adjustable User Input
Python Logic: N/A
Live Evaluation: N/A (Input Variable)
\( W_{\text{chain, sidewall}} \) Chain Sidewall Thickness (m) 0.000000
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Purpose: Wall Gauge Thickness.
Logic: Calculates the minimum physical thickness of the outer link flaps to sustain operational chain tension loops.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
SQRT ( ( Tangential Drive Force (N) / 2 ) / ( Carbon Fibre Tensile Limit (Mpa) * 10^6 * Chain Side-Wall Hug Depth (m) ) )
Python Logic: N/A
Live Evaluation: N/A
\( \Sigma W_{\text{ext, chain}} \) Total External Chain Width (m) 0.000000
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Purpose: Maximum Outer Width.
Logic: The final, absolute maximum spatial cross-sectional envelope of the moving chain loop assembly.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Internal Channel Width (m) + ( Sidewall Running Clearance (m) * 2) + ( Chain Sidewall Thickness (m) * 2)
Python Logic: N/A
Live Evaluation: N/A
\( H_{\text{ext, chain}} \) External Chain Top Height (m) 0.000000
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Purpose: Crown Structural Depth.
Logic: The solid material height directly above the gear rim to securely house and reinforce the central pin bore.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Calculated Pin Diameter (m) * Pin Safety Factor
Python Logic: N/A
Live Evaluation: N/A
\( \Sigma H_{\text{ext, chain}} \) Total External Chain Height (m) 0.000000
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Purpose: Total Link Profile Height.
Logic: The absolute vertical dimension of an individual articulating box-link casing from top to bottom.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Chain Side-Wall Hug Depth (m) + External Chain Top Height (m)
Python Logic: N/A
Live Evaluation: N/A
\( \theta_{\text{req, taper}} \) Required Taper Angle (Degrees) 0.000000
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Purpose: Wedge Relief Angle.
Logic: The precise trapezoidal cutback required on the link edges so the flaps can clear each other smoothly when rounding the wheels.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
DEGREES ( ATAN ( Chain Pitch (m) / (Gear Radius (m) - Chain Side-Wall Hug Depth (m) ) ) ) - DEGREES ( ATAN ( Chain Pitch (m) / Gear Radius (m) ) )
Python Logic: N/A
Live Evaluation: N/A
\( \Sigma W \) Total width (m) 0.000000
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Purpose: System Footprint Envelope.
Logic: Combines the skeleton length boundaries and rail widths with the chain envelope to track master lane clearances.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
( GMEG Length (m) * 2 ) + ( Prescribed Rail Width (m) * 2 ) + Total External Chain Width (m)
Python Logic: N/A
Live Evaluation: N/A
Central Enabler Pin Component
\( \Sigma F_{\text{linear, drive}} \) Total Linear Drive Force (N) 0.000000
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Purpose: Total System Loop Load.
Logic: Links the total macro directional driving force down to the mechanical connection axles.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Tangential Drive Force (N)
Python Logic: N/A
Live Evaluation: N/A
\( N_{\text{active, pins}} \) Number of Active Enabler Pins 0.000000
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Purpose: Load-Bearing Anchors.
Logic: The number of continuous central rods actively distributing the total transit pull force.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
GMEG Gravity Enablers
Python Logic: N/A
Live Evaluation: N/A
\( F_{\text{individual, pin}} \) Force Per Individual Pin (N) 0.000000
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Purpose: Pin Shear Load.
Logic: The raw concentrated cutting force focused on a single structural axle shaft connection point.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Total Linear Drive Force (N) / Number of Active Enabler Pins
Python Logic: N/A
Live Evaluation: N/A
\( \tau_{\text{shear, plane}} \) Shear Plane Plane Factor
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Purpose: Double Shear Identifier.
Logic: Accounts for continuous rod layout, splitting the shearing stress perfectly across two separate material planes.
Type: Manual Entry
Render on Grids: None
Mathematical Formula:
Adjustable User Input
Python Logic: N/A
Live Evaluation: N/A (Input Variable)
\( SF_{\text{pin, safety}} \) Pin Safety Factor 0.000000
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Purpose: Dave-Proof Cushion.
Logic: Structural design buffer to confidently manage unexpected transient deceleration or extreme load spikes.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Safety Factor Slider
Python Logic: N/A
Live Evaluation: N/A
\( X_{\text{req, pin}} \) Required Pin Cross-Section (m2) 0.000000
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Purpose: Axle Cross-Sectional Volume.
Logic: The physical solid material surface area required inside the pin body to resist tearing or shearing apart.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
( Force Per Individual Pin (N) * Pin Safety Factor ) / ( 2 * Carbon Fiber Shear Limit (MPa) * 10^6)
Python Logic: N/A
Live Evaluation: N/A
\( D_{\text{calculated, pin}} \) Calculated Pin Diameter (m) 0.000000
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Purpose: The Final Pin Gauge.
Logic: The ultra-precise, solid pin thickness requirement.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
SQRT ( ( 4 * Required Pin Cross Section (m2) ) / PI() )
Python Logic: N/A
Live Evaluation: N/A
U-Chain Mass
\( L_{\text{straight, track}} \) Straight Track Length (m) 6.000000
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Purpose: The Flat Run.
Logic: The direct linear distance of the flat track section spanning between the two large gear centers.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
DLLS Straight track length (m)
Python Logic: N/A
Live Evaluation: N/A
\( \Sigma L_{\text{chain, loop}} \) Total Chain Loop Length (m) 0.000000
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Purpose: Total Loop Perimeter.
Logic: The absolute continuous length of the entire articulating chain loop wrapping the system.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
DLLS Track full run length (m)
Python Logic: N/A
Live Evaluation: N/A
\( A_{\text{link, crosssectional}} \) Link Cross-Sectional Area (m2) 0.000000
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Purpose: The U-Shape Profile.
Logic: The actual material end-face area of the hollow inverted "U" cap, subtracting the core cutout channel where the gear sits.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
( Total External Chain Width (m) * Total External Chain Height (m)) - (Internal Channel Width (m) * Chain Side-Wall Hug Depth (m) )
Python Logic: N/A
Live Evaluation: N/A
\( M_{\text{chain, unit}} \) Chain Unit Mass (kg/m) 0.000000
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Purpose: Linear Weight Profile.
Logic: The calculated physical mass of the heavy-duty box chain per linear meter of length.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Link Cross-Sectional Area (m2) * Carbon Fiber Density (kg/m3)
Python Logic: N/A
Live Evaluation: N/A
\( L_{\text{links, chain}} \) Links per chain loop length 0.000000
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Purpose: Total Link Count.
Logic: The exact number of individual physical modular block links required to assemble the full closed drive loop.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Total Chain Loop Length (m) / Chain Pitch (m)
Python Logic: N/A
Live Evaluation: N/A
\( \Sigma M_{\text{chain}} \) Total Chain Mass (kg) 0.000000
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Purpose: Total Chain Loop Weight.
Logic: The final aggregated weight of the entire moving, articulating loop assembly circling the GMEG track structure.
Type: Calculated (Math Output)
Render on Grids: None
Mathematical Formula:
Total Chain Loop Length (m) * Chain Unit Mass (kg/m)
Python Logic: N/A
Live Evaluation: N/A