The blue input shaft slides along its axis while rotating, passing both motions to three yellow output shafts. Spur-gear pairs reverse and scale the rotation, while blue flange couplings carry the axial movement. Use the calculator to compare stroke, angular travel and cycle speed for this combined-motion transmission.
Rectilinear Motion Interactive Calculator
Set the axial stroke, input-turn amplitude, tooth counts and cycle rate. The three output shafts share the axial stroke; their rotary travel follows the gear ratio. The diagram separates the side view of sliding motion from an end view of one gear pair.
Equation Used
- Stroke is peak-to-peak and the selected phase law is sinusoidal.
- All three output stations are identical and remain engaged through the selected axial travel.
- External spur gears use the entered tooth counts only for an ideal angular ratio.
- The entered dimensions and tooth counts define this demonstration; they are not manufacturing specifications or operating ratings.
How sliding and rotary motion pass to the outputs
An external drive gives the long blue shaft axial travel and rotation. At each output station, an external spur-gear pair transfers the rotation to a yellow shaft. The blue flange coupling carries that output assembly along with the axial input movement.
Each gear pair reverses the direction of rotation. With driver tooth count Nd and output count No, the ideal relation is θo=−(Nd/No)θi. The flange coupling is treated as rigid, so each output has the same axial displacement as the input.
The side view shows axial movement at all three stations. The end-view inset shows rotation of one representative pair. The tooth outlines are schematic; they are not machining profiles.
Comparing combined shaft motion
Use this example to study how one input can distribute sliding and rotary motion to several shafts. Changing the tooth ratio alters the output turn amplitude without changing the shared axial stroke. Changing cycle rate alters the motion timing and maximum axial speed.
The calculator assumes identical output stations and perfect axial following. A real assembly also needs gear, shaft, coupling, bearing and housing design. It does not calculate torque, contact stress, backlash, friction, wear or required power.
Sinusoidal travel and gear ratio
Let the entered axial stroke be the peak-to-peak value S and let phi be cycle phase. The selected input displacement is x = (S/2) sin(phi). If T is the entered input-turn amplitude, thetai = 2 pi T sin(phi). Each external spur pair gives thetao = -(Nd/No) thetai.
At n cycles per minute, the maximum axial speed of this selected sinusoid is vmax = pi S n / 60. The sine function defines this demonstration’s timing. It is not a measured motion record from the video.
Worked example
With an 80 mm peak-to-peak stroke, one input-turn amplitude, an 18-tooth driver and a 24-tooth output gear, each output follows the same 80 mm stroke and has a 0.75-turn angular amplitude in the opposite direction. At 10 cycles per minute, each cycle takes 6 seconds and maximum axial speed is 41.9 mm/s. The axial position ranges from −40 to +40 mm; output rotation ranges from −0.75 to +0.75 turns about its middle position.
What the ideal motion leaves out
The animation keeps all three stations engaged and gives their shafts equal axial displacement. Clearances, deflection and backlash can change how an actual assembly follows the input, especially at reversal.
The external drive is not part of the illustrated assembly. The input stroke, turn amplitude, tooth counts and cycle rate are values to explore, not a specification for building the video mechanism. Check loads, support spacing, gear engagement and coupling clearances before developing a physical design.
Combined-motion questions
Where does the input motion come from?
An external drive moves and rotates the blue shaft. It is outside the illustrated assembly. The calculator uses a sinusoidal input to show how both motions pass to the outputs.
Why do the yellow shafts rotate the other way?
Each station uses an external spur-gear pair, so its output rotates opposite the input. The magnitude of the angular ratio is the blue tooth count divided by the yellow tooth count.
What does input-turn amplitude mean?
It is the maximum rotation away from the middle position. An amplitude of one turn means motion from −1 to +1 turns, a two-turn sweep between extremes. Axial stroke is different: it is already the full travel from one axial extreme to the other.
Do the entered tooth counts reproduce the video?
The tooth-count inputs let you compare ideal ratios. They are not dimensions or specifications for the illustrated video mechanism.
Why do the result cards stay constant during playback?
They give full stroke, turn amplitude, gear ratio and maximum axial speed for the entered inputs. The diagram readouts show the current offset and angles as the shafts move.
Does the calculator size the mechanism?
No. It calculates ideal motion, not torque, strength, fit, wear, bearing load or power. The gears, shafts, couplings and supports need their own load and clearance calculations.
Technical references
- Nguyen Duc Thang, Transmission of rectilinear and rotary motion — identifies the blue combined-motion input, yellow output shafts, spur-gear drives, blue flanges and omitted external source.
- KHK, Direction of Rotation of Gears — external spur-gear pairs rotate in opposite directions.
- KHK, Calculation of Gear Dimensions — reference-circle and tooth-count relationships for standard spur gears.
- OpenStax University Physics, Position and Displacement — one-dimensional position and displacement definitions.
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