A differential micrometer screw combines two same-hand thread leads. The output moves by their difference, allowing a small adjustment when the two leads are close.
Same-Hand Differential Screw Calculator
Enter two same-hand lead magnitudes and signed screw turns. The worksheet separates shaft advance, moving-nut motion relative to the screw and net output relative to the frame; it assumes both nuts cannot rotate.
Equation Used
- Both thread sections are single-start, coaxial and the same hand.
- The frame nut and output nut are prevented from rotating.
- The screw can translate axially through the fixed nut while it rotates.
- Backlash, elastic deformation, friction, torque, load, pitch error and end limits are excluded.
The calculator separates shaft motion through the fixed nut from output-nut motion along the shaft. Their algebraic sum gives the output displacement relative to the frame.
Two leads, two constraints, one differential output
A same-hand differential screw has two thread sections on one shaft. One engages a nut fixed to the frame; the other engages an output nut that cannot rotate but can translate. One screw turn advances the shaft through the fixed nut by L1 while the output nut walks back along the screw by L2. Relative to the frame, the motions add algebraically to L1-L2.
Calculating ideal displacement
Use the calculator to find signed component and output motion. It does not select threads, predict resolution or accuracy, carry load, assess strength or guarantee freedom from backlash.
Same-hand differential motion
If L2 exceeds L1, the signed output reverses. Opposite-hand threads produce additive rather than subtractive motion and are outside this worksheet.
Differential-motion example
For L1=0.50 mm/rev, L2=0.45 mm/rev and one turn, the shaft advances +0.500 mm, the output nut moves -0.450 mm relative to the screw and the output advances +0.050 mm relative to the frame.
Ideal motion is not precision performance
MIT notes that a real differential screw must accommodate shaft translation and that avoiding backlash can be difficult. Actual performance depends on thread accuracy, nut design, preload, alignment, bearings, coupling, load and measurement method.
Differential-screw questions
Why can the output be much smaller than the thread motions?
The same-hand component motions oppose each other. When the leads are close, their difference is small.
Can the sign reverse?
Yes. If L2 is greater than L1, the ideal output moves opposite the shaft advance.
Does a 50 micrometre effective lead guarantee 50 micrometre accuracy?
No. It is ideal motion per revolution, not a tolerance or calibration claim.
Engineering references
- MIT, FUNdaMENTALS of Design, Topic 6: differential leads, virtual lead, fixed-nut constraint and translating screw-shaft requirement.
- B. S. Ramprasad, A Simple Differential Micrometer Head: net motion equals the difference between two screw pitches.
- US4373404A, Differential screw actuator: differential motion from differing threaded engagements.
- TeachSpin, Modern Interferometry manual: differential micrometer displacement as the difference of internal and external thread motion.
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