Set the pizza diameter, edge thickness and gap between rows.
Adjust the sliders to see the effects immediately: the motion-scope curve profiles, chart values, calculated travel, timing and forces update in real time. Watch the crosshead at normal or quarter speed to understand the downstroke, return and raised dwell.
Calculation basis: classical mechanics—Newton’s second law (F = ma), gravity, CAD volume × material density, and a defined quintic motion profile. Cycle RMS force includes the raised dwell. View equations and references.
Default sizing allowance: +20% (factor 1.20). Calculated CAD weight stays unfactored; the scope uses the weight with the selected allowance. The upper chassis has space for up to four motors; final motor count and coordinated load sharing require supplier review.
Pizza & cut settings
Crosshead & blade motion
Where the cut lands
edge
leading edge
Motion scope
Compare 2-inch and 4-inch gaps
Both rows use the selected pizza diameter, thickness, blade, clearance, speed and allowance. A cut distance above 1 inch is limited to 1 inch in the 2-inch-gap comparison.
| Gap / pitch | Cut behind pizza in | Down / up ms | Raised dwell ms | Cycles/min | Peak speed m/s | Peak accel g | Calculated load peak lbf | With allowance peak lbf / N | With allowance cycle RMS lbf |
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Calculated moving weight · component inventory
Calculated from STEP solid volumes and assigned densities, with no safety factor applied to these component weights. Source: Crosshead and Blade for weight.step · 27 valid solids · 249.947 in³. All exported bodies are included initially. Confirm moving parts and material assignments; group names are geometric interpretations.
| Include / component (solid IDs) | Volume in³ | Aluminum | Calculated weight lb |
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What the controls mean
Pizza diameter and gap determine how often a row arrives: pitch = diameter + gap. At 50 FPM, the belt moves 10 inches per second. A 2-inch gap passes in 200 ms; a 4-inch gap passes in 400 ms.
Total blade travel = actual pizza edge thickness + additional clearance above that edge + blade overtravel needed to complete the cut. The return covers the same distance. Clearance presets are your suggested operating assumptions; overtravel values are your supplied blade assumptions.
Cut point means the completed cut at the bottom reversal. In this simplified model the blade starts its entire downstroke when the trailing edge clears, and finishes its return when the next leading edge reaches the blade. Down time = cut distance ÷ belt speed; up time = remaining gap ÷ belt speed. At 50 FPM and a 1-inch cut distance: a 2-inch gap allows 100 ms down + 100 ms up; a 4-inch gap allows 100 ms down + 300 ms up. The 1-inch preference in a 4-inch gap is intentionally off-center. Zero cut distance provides zero downstroke time and cannot produce a finite motion.
Timing boundary: this uses the full clear gap, with no additional allowance for sensing error, blade width, product variation or lane stagger. Additional clearance is included in total travel, with no credit for starting above the preceding pizza. This is a conservative geometric scheduling assumption, not a validated collision-clearance or control schedule. Raising the weight allowance does not add timing clearance.
Calculated weight vs sizing weight: calculated weight is CAD volume × assigned density, not a scale measurement. It remains unfactored. Sizing weight = calculated weight × (1 + selected allowance/100). At 20%, the multiplier is 1.20. The force scope uses sizing weight; the comparison also shows the unfactored calculated-load peak. The selected allowance does not replace actual motor-slider/coupler mass, measured cutting force, friction, cable drag, supplier design factors or a structural safety assessment.
Engineering equations, units & references
The force balance follows Newton’s second law (NASA reference). The specific quintic curve and RMS expression below are the mathematical model implemented here. LinMot’s sizing tutorial explains why the full motion cycle, including standstill, moving motor mass and thermal limits must be considered. These references support the principles; this calculator is not represented as an ASME-certified calculation or a reproduction of a specific Machinery’s Handbook method.
Each direction uses a quintic rest-to-rest curve p(u) = 10u³ − 15u⁴ + 6u⁵, u = 0…1. Down: x = S·p(t/t↓). Up: x = S·[1 − p((t−t↓)/t↑)]. Velocity and acceleration are zero at reversal; there is no programmed bottom dwell. For each direction with duration h: v_peak = 1.875S/h and a_peak = (10/√3)S/h². Unequal down/up times produce unequal velocity and acceleration peaks. Phase 0–180° is down; 180–360° is up, so phase speed is not uniform when their durations differ.
Motor force positive upward: F = m(g − a_down), g = 9.80665 m/s². Peak absolute force = m(g + max|a|). Cycle RMS = m√[g² + (120/7)S²(1/t↓³ + 1/t↑³)/P], where P is the row period. Powered upper dwell holds mg; no counterbalance is assumed. Jerk is finite within each segment but discontinuous at transitions. Actual motor programming may require a different profile.
Linear inertia is mass in kg or slug; force is N or lbf. Energy is J or ft·lbf. Rotational inertia is kg·m² and is not the direct-drive linear sizing quantity. All forces are total assembly demand. The upper chassis can accommodate up to four motors. Dividing total force by 2, 3 or 4 gives only an ideal equal-share estimate; actual slider mass, motor spacing, crosshead stiffness, synchronization, force at speed and thermal duty must be reviewed for the chosen arrangement. A 20% mass allowance is a preliminary sizing assumption, not evidence that the final motor has adequate reserve.
Rotational values use the checked CAD bodies only, before the allowance, about their combined center of mass. X is along the span, Y through thickness, Z approximately vertical.
Material and geometry basis
Aluminum density: 2,700 kg/m³ (6061-T6). Retained blade and hardware: 7,900 kg/m³ steel proxy, not a blade-hardness or alloy specification. Calculated weight is the sum of solid volumes × assigned density; there is no overlap deduction. No new blade geometry or motor mass is introduced by choosing a blade type. The displayed supplied blade is about 48.04 inches wide. Material substitutions still require stiffness, alignment and fatigue checks.
Sources: Outokumpu steel density; thyssenkrupp 6061 density. This is a calculated comparison, not a validated LinMot operating envelope.