![DifferentialScrew](https://upload.wikimedia.org/wikipedia/commons/c/c8/DifferentialScrew.gif)
A differential screw is a
mechanism
Mechanism may refer to:
*Mechanism (engineering), rigid bodies connected by joints in order to accomplish a desired force and/or motion transmission
*Mechanism (biology), explaining how a feature is created
*Mechanism (philosophy), a theory that a ...
used for making small, precise adjustments to the spacing between two objects (such as in focusing a
microscope
A microscope () is a laboratory instrument used to examine objects that are too small to be seen by the naked eye. Microscopy is the science of investigating small objects and structures using a microscope. Microscopic means being invisibl ...
,
["A ONE-DOLLAR COMPOUND MICROSCOPE"](_blank)
/ref> moving the anvils of a micrometer Micrometer can mean:
* Micrometer (device), used for accurate measurements by means of a calibrated screw
* American spelling of micrometre
The micrometre ( international spelling as used by the International Bureau of Weights and Measures; ...
, or positioning optics). A differential screw uses a spindle
Spindle may refer to:
Textiles and manufacturing
* Spindle (textiles), a straight spike to spin fibers into yarn
* Spindle (tool), a rotating axis of a machine tool
Biology
* Common spindle and other species of shrubs and trees in genus ''Euony ...
with two screw threads of differing leads
Lead is a chemical element with symbol Pb and atomic number 82.
Lead or The Lead may also refer to:
Animal handling
* Leash, or lead
* Lead (leg), the leg that advances most in a quadruped's cantering or galloping stride
* Lead (tack), a lin ...
(in case of a single lead equal to the thread pitch), and possibly opposite handedness
In human biology, handedness is an individual's preferential use of one hand, known as the dominant hand, due to it being stronger, faster or more Fine motor skill, dextrous. The other hand, comparatively often the weaker, less dextrous or sim ...
, on which two nuts move. As the spindle rotates, the space between the nuts changes based on the difference between the threads. These mechanisms allow extremely small adjustments using commonly available screws. A differential screw mechanism using two nuts incurs higher friction and therefore requires more torque to turn than a simple, single lead screw with an equivalent pitch.
History
The first known use of a differential screw was on Towneley’s version of Gascoigne’s Micrometer.
''Flamsteed’s Preface to the Historia Coelestis Britannica:''
"Richard Towneley ... carried forward and completed his instrument (the micrometer) and made it perform with one screw, what on Gascoigne’s instrument had required two.”
A drawing by Robert Hooke in 1667 clearly shows Towneley’s Micrometer with the single screw with two different pitch threads on it. With this differential screw, one thread was half the pitch of the other, Towneley was able to keep the micrometer's indicating pointers centered in the field of view as they opened and closed.
Examples
Many differential screw configurations are possible. The micrometer adjuster pictured uses a nut sleeve with different inner and outer thread pitches to connect a screw on the adjusting rod end with threads inside the main barrel; as the thimble rotates the nut sleeve, the rod and barrel move relative to each other based on the differential between the threads.
Another arrangement holds the two " nuts" co-axially in a single fixture and has two separate screw
A screw and a bolt (see '' Differentiation between bolt and screw'' below) are similar types of fastener typically made of metal and characterized by a helical ridge, called a ''male thread'' (external thread). Screws and bolts are used to fa ...
s with slightly different pitches (distance from the crest of one thread to the next) entering from opposite ends. The "heads" of the screws are fixed to the two objects whose spacing is to be adjusted. Each rotation of the fixture holding the nuts moves one screw into its nut by a small amount and moves the other screw out of its nut by a slightly larger amount. The total spacing between the screws, and thus the objects, will be slightly changed based on the difference in travel between the two screws.
More arrangements are possible. Two nuts can be fixed to each of two objects to be adjusted and the two screw heads attached to each other in the middle. The combined screws would be turned to adjust the spacing in that case.
Calculating motion and effective thread pitch
For single start threads, each turn changes the distance between the nuts by the effective pitch, . For a bolt with a given thread per inch, on one end and a second thread per inch, on the other, the change in distance (or ), and the effective thread per inch , is calculated by:
For example, a bolt with coarse threads (16 tpi, per turn) on one end and fine threads (24 tpi, per turn) on the other changes the distance between the nuts by about per revolution and is equivalent to a 48 tpi (0.53 mm/thread) thread:
For single start Metric threads, the effective pitch is simply the difference between the two thread pitches:
{{math, Pitch{{ssub, 1 - Pitch{{ssub, 2 {{= Pitch{{ssub, eff
For example, an M5x0.80 thread paired with an M4x0.70 thread will produce a differential motion of 0.1 mm, or 100 microns per revolution.
Mixing metric and imperial threads can result in finer differentials while still using standard threads, they can be calculated in the same way as a metric differential but the TPI of the imperial thread must be converted to a metric pitch measurement. For example a 26 TPI thread has a pitch of ~0.977mm and when paired with a 1.0mm pitch metric thread the differential motion will be approximately 0.023mm per revolution.
References
Mechanisms (engineering)
Metalworking
Screws