Oblique rollers move a sheet forward while urging it toward a straight marginal guide. Explore the conveyor arrangement described in US patent 3,763,992 and calculate ideal forward and guideward motion from the roller-surface velocity.
Ideal Oblique-Roller Motion Calculator
Enter a declared roller-surface speed, surface-velocity skew angle, longitudinal bed length and starting gap to the guide. The worksheet resolves ideal vector components and geometric travel only; it does not model traction, slip, impacts or package dynamics.
Equation Used
- The roller surface has declared speed V and its ideal velocity direction is skewed by theta from longitudinal travel.
- The sheet follows the surface-velocity vector without slip until it reaches the straight marginal guide.
- The longitudinal bed length and starting guide gap are declared geometry, not dimensions recovered from the patent.
- Roller diameter, spacing, drive arrangement, sheet stiffness, friction, slip, skew compliance, guide impact, jams, loads, power, wear, controls, throughput and safety are excluded.
The roller-surface velocity is resolved into forward and guideward components. The model assumes the sheet follows that direction without slip until it reaches the guide.
Oblique rollers advance a sheet while urging it toward a marginal guide
US patent 3,763,992 describes driven oblique rollers whose axes form an acute angle open toward the destination and a straight marginal guide. Their surface motion gives the sheet a forward component and a component toward that guide.
The viewer shows this connected plan-view topology and stops ideal lateral motion at the guide.
Sheet alignment against a marginal guide
The patent describes a conveyor table particularly for sheet material, including paper, and uses the marginal guide as a reference edge. The calculation illustrates ideal sheet motion; it does not predict tracking accuracy or throughput for a particular conveyor.
Ideal no-slip vector construction
Because traversal time is L/Vx, unconstrained lateral travel is Vy(L/Vx)=L tanθ. Actual material motion can differ because the sheet-guide-roller contact system is not ideal.
Declared geometry example
For V=1.0 m/s, θ=7°, L=1.0 m and g=100 mm, ideal components are 0.993 m/s forward and 0.122 m/s guideward. Unconstrained lateral travel is 122.8 mm and the ideal longitudinal length needed to close the gap is 0.814 m.
Ideal motion and actual sheet tracking
The entered speed is the magnitude of the roller-surface velocity, not its forward component. Real sheet motion can differ because of slip, flexibility and contact with the guide. The ideal travel calculation does not determine contact forces, alignment accuracy or suitable operating conditions.
Oblique-roller questions
Is V the forward conveyor speed?
No. V is the declared magnitude of the ideal surface-velocity vector; its forward component is V cosθ.
Does the calculator predict real sheet tracking?
No. It assumes no slip and reports geometry only.
What happens after the sheet reaches the guide?
The animation constrains lateral position at the guide; real contact forces and slip are outside the model.
Oblique-roller references
- US Patent 3,763,992, Conveyor table for sheet material: primary source for driven oblique rollers, acute axis orientation and the straight marginal guide.
- OpenStax University Physics, vector components: standard sine/cosine resolution used in the declared ideal model.
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