Differential screw

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Rotating a bolt through two nuts with slightly different thread pitches for each changes the separation of the nuts by the difference between the threads. DifferentialScrew.gif
Rotating a bolt through two nuts with slightly different thread pitches for each changes the separation of the nuts by the difference between the threads.
Micrometer adjuster with differential threads. The threads 11 on rod 4 have one pitch (e.g. 25 tpi, blue), while the threads 10 in the barrel 1 have another (e.g. 20 tpi, orange). A full turn of the thimble 12 rotates the nut sleeve 13 and its two threads (20 tpi outside and 25 tpi inside) to move the rod /20 -  /25 = 0.01 in (0.25 mm) relative to the barrel. Differential adjuster from patent 585184 fig 1, 2.png
Micrometer adjuster with differential threads. The threads11on rod4have one pitch (e.g. 25 tpi, blue), while the threads10in the barrel1have another (e.g. 20 tpi, orange). A full turn of the thimble12rotates the nut sleeve13and its two threads (20 tpi outside and 25 tpi inside) to move the rod /20 -  /25 = 0.01 in (0.25 mm) relative to the barrel.
Differential screw illustration from an 1817 machine design handbook. ab & ef have one thread pitch while cd has a different one. One turn of AB moves the whole spindle one ab thread distance; simultaneously, M moves one cd thread distance and the amount that AB moved. M's overall movement is thus the difference between ab and cd. Lanz & Betancourt- Analytical essays on the construction of machines, pg 181 - Plate 1 - Fig D3.png
Differential screw illustration from an 1817 machine design handbook. ab & ef have one thread pitch while cd has a different one. One turn of AB moves the whole spindle one ab thread distance; simultaneously, M moves one cd thread distance and the amount that AB moved. M's overall movement is thus the difference between ab and cd.
Differential screw leveling feet, drawing by Joshua Rose, 1887. Differential Screw Leveler, Modern Machine-Shop Practice, Vol. I (of 2), by Joshua Rose, Figure 417, 1887 - illo0135e.png
Differential screw leveling feet, drawing by Joshua Rose, 1887.

A differential screw is a mechanism used for making small, precise adjustments to the spacing between two objects (such as in focusing a microscope, [2] moving the anvils of a micrometer, [3] [4] or positioning optics [5] ). A differential screw uses a spindle with two screw threads of differing leads (in case of a single lead equal to the thread pitch), and possibly opposite handedness, 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. [6] [7] [8]

Contents

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.” [9]  

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. [10]

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 screws 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. [1]

Calculating motion and effective thread pitch

For single start threads, each turn changes the distance between the nuts by the effective pitch, Peff. For a bolt with a given thread per inch, TPI1 on one end and a second thread per inch, TPI2 on the other, the change in distance (or Peff), and the effective thread per inch TPIeff, is calculated by:

1/TPI1 - 1/TPI2 = 1/TPIeff = Peff [11]

For example, a bolt with coarse threads (16 tpi, 0.0625 in [1.59 mm] per turn) on one end and fine threads (24 tpi, 0.0416 in [1.06 mm] per turn) on the other changes the distance between the nuts by about 0.02 inches (0.51 mm) per revolution and is equivalent to a 48 tpi (0.53 mm/thread) thread:

1/16 - 1/24 = 0.0208 in. (48 tpi, 0.53 mm/thread)

For single start Metric threads, the effective pitch is simply the difference between the two thread pitches:

Pitch1 - Pitch2 = Pitcheff

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.

Related Research Articles

<span class="mw-page-title-main">Micrometer (device)</span> Tool for the precise measurement of a components length, width, and/or depth

A micrometer, sometimes known as a micrometer screw gauge, is a device incorporating a calibrated screw widely used for accurate measurement of components in mechanical engineering and machining as well as most mechanical trades, along with other metrological instruments such as dial, vernier, and digital calipers. Micrometers are usually, but not always, in the form of calipers. The spindle is a very accurately machined screw and the object to be measured is placed between the spindle and the anvil. The spindle is moved by turning the ratchet knob or thimble until the object to be measured is lightly touched by both the spindle and the anvil.

<span class="mw-page-title-main">Tap and die</span> Tools to create screw threads

Taps and dies are tools used to create screw threads, which is called threading. Many are cutting tools; others are forming tools. A tap is used to cut or form the female portion of the mating pair. A die is used to cut or form the male portion of the mating pair. The process of cutting or forming threads using a tap is called tapping, whereas the process using a die is called threading.

The Unified Thread Standard (UTS) defines a standard thread form and series—along with allowances, tolerances, and designations—for screw threads commonly used in the United States and Canada. It is the main standard for bolts, nuts, and a wide variety of other threaded fasteners used in these countries. It has the same 60° profile as the ISO metric screw thread, but the characteristic dimensions of each UTS thread were chosen as an inch fraction rather than a millimeter value. The UTS is currently controlled by ASME/ANSI in the United States.

<span class="mw-page-title-main">William Gascoigne (scientist)</span> 17th-century English astronomer, mathematician, and scientist

William Gascoigne was an English astronomer, mathematician and maker of scientific instruments from Middleton, Leeds who invented the micrometer and the telescopic sight. He was one of a group of astronomers in the north of England who followed the astronomy of Johannes Kepler, which included Jeremiah Horrocks and William Crabtree.

<span class="mw-page-title-main">Cage nut</span>

A cage nut or caged nut consists of a nut in a spring steel cage which wraps around the nut. The cage has two wings that when compressed allow the cage to be inserted into the square holes, for example, in the mounting rails of equipment racks. When the wings are released, they hold the nut in position behind the hole. Cage nuts conforming to this description were patented in 1952 and 1953. The original design requires an insertion tool to install a cage nut into a hole. Newer designs featuring squeeze-and-release tabs allow for tool-less installation.

<span class="mw-page-title-main">Screw thread</span> Helical structure used to convert between rotational and linear movement or force

A screw thread is a helical structure used to convert between rotational and linear movement or force. A screw thread is a ridge wrapped around a cylinder or cone in the form of a helix, with the former being called a straight thread and the latter called a tapered thread. A screw thread is the essential feature of the screw as a simple machine and also as a threaded fastener.

British Standard Whitworth (BSW) is an imperial-unit-based screw thread standard, devised and specified by Joseph Whitworth in 1841 and later adopted as a British Standard. It was the world's first national screw thread standard, and is the basis for many other standards, such as BSF, BSP, BSCon, and BSCopper.

<span class="mw-page-title-main">Trapezoidal thread form</span> Screw thread profiles with trapezoidal outlines

Trapezoidal thread forms are screw thread profiles with trapezoidal outlines. They are the most common forms used for leadscrews. They offer high strength and ease of manufacture. They are typically found where large loads are required, as in a vise or the leadscrew of a lathe. Standardized variations include multiple-start threads, left-hand threads, and self-centering threads.

<span class="mw-page-title-main">Lug nut</span> Fastener, specifically a nut, used to secure a wheel on a vehicle

A lug nut or wheel nut is a fastener, specifically a nut, used to secure a wheel on a vehicle. Typically, lug nuts are found on automobiles, trucks (lorries), and other large vehicles using rubber tires.

British Standard Brass or British Brass Thread is an imperial unit based screw thread. It adopts the Whitworth thread form with a pitch of 26 threads per inch and a thread angle of 55 degrees for all diameters. It is often wrongly called British Standard Brass but is not actually covered by a British Standard.

The ISO metric screw thread is the most commonly used type of general-purpose screw thread worldwide. They were one of the first international standards agreed when the International Organization for Standardization (ISO) was set up in 1947.

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Computer case screws are the hardware used to secure parts of a PC to the case. Although there are numerous manufacturers of computer cases, they have generally used three thread sizes. The Unified Thread Standard (UTS) originates from the United States, while the ISO metric screw thread is standardized worldwide. In turn, these thread standards define preferred size combinations that are based on generic units—some on the inch and others on the millimetre.

<span class="mw-page-title-main">Screw</span> Type of fastener characterized by a thread wrapped around a cylinder core

A screw is an externally helical threaded fastener capable of being tightened or released by a twisting force (torque) to the head. The most common uses of screws are to hold objects together and there are many forms for a variety of materials. Screws might be inserted into holes in assembled parts or a screw may form its own thread. The difference between a screw and a bolt is that the latter is designed to be tightened or released by torquing a nut.

ISO 898 is an international standard that defines mechanical and physical properties for metric fasteners. This standard is the origin for other standards that define properties for similar metric fasteners, such as SAE J1199 and ASTM F568M. It is divided into five (nonconsecutive) parts:

<span class="mw-page-title-main">Roller screw</span> Low-friction precision screw-type actuato

A roller screw, also known as a planetary roller screw or satellite roller screw, is a low-friction precision screw-type actuator, a mechanical device for converting rotational motion to linear motion, or vice versa. Planetary roller screws are used as the actuating mechanism in many electromechanical linear actuators. Due to its complexity, the roller screw is a relatively expensive actuator, but may be suitable for high-precision, high-speed, heavy-load, long-life, and heavy-use applications.

<span class="mw-page-title-main">Bolt (fastener)</span> Threaded fastener with an external male thread requiring a matching female thread

A bolt is an externally helical threaded fastener that fastens objects with unthreaded holes together. This is done by applying a twisting force (torque) to a matching nut. The bolt has an external male thread requiring a matching nut with a pre-formed female thread. Unlike a screw, which holds objects together by the restricting motion parallel to the axis of the screw via the normal and frictional forces between the screw's external threads and the internal threads in the objects to be fastened, a bolt prevents that linear motion via the frictional and normal forces between the bolt's external threads and the internal threads of the matching nut, which can be tightened by applying a torque which moves the nut linearly along the axis of the bolt and compresses the objects to be fastened.

<span class="mw-page-title-main">Fine adjustment screw</span>

A fine adjustment screw is a screw with threads between 40 and 100 threads per inch (TPI); 0.5–0.2 mm pitch. An ultra-fine adjustment screw has 100–508 TPI. Even though these are non-standard threads, both ISO metric screw thread designations and UNC designations have been used to call out thread dimensions and fit (class). A typical use for a fine adjustment screw is in an optical mirror mount as an adjuster. Typically, 80 TPI screws are used in mirror mounts. Ultra-fine adjustment screws are used in applications requiring extremely fine motion, like laser alignment and fiber coupling.

<span class="mw-page-title-main">M-LOK</span> Firearm rail interface system

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<span class="mw-page-title-main">Wrench size</span>

Width across flats is the distance between two parallel surfaces on the head of a screw or bolt, or a nut, mostly for torque transmission by positive locking.

References

  1. 1 2 José María de Lanz; Agustín de Betancourt (1817). Analytical essay on the construction of machines: translated from the French of M.M. Lanz and Bétancourt. London: R. Ackermann. pp. 14–15, 181 Plate 1 fig D3.
  2. "A ONE-DOLLAR COMPOUND MICROSCOPE"
  3. USpatent 343478,McArthur, Duncan,"Micrometer Calipers",issued 1880-02-08
  4. "Micrometer Heads Series 110-Differential Screw Translator (extra-Fine Feeding) Type". Product Catalog. Mitutoyo, U.S.A. Archived from the original on November 9, 2011. Retrieved December 11, 2012.
  5. "Tutorials: Opto-Mechanical Components, Translation Stages, Drive Options". Archived from the original on 2010-01-15. Retrieved 2012-12-14.
  6. "Screw Threads - The Theory Of Machines - Engineering Reference with Worked Examples" . Retrieved 2012-12-24.
  7. Kostelnicek, Dick (March 2010). "That Ol' Differential Screw Clamp" (PDF). Home Metal Shop Club Newsletter. 5 (3): 5–6. Retrieved 2012-12-24.
  8. Kuhrt, O.C. (1916). "A Toolmaker's Novel Clamp". American Machinist . 44: 32.
  9. Williams, Mari E. W. (1985). "John Flamsteed, Preface to Historia Coelestis Britannica. Edited and introduced by Allan Chapman, based on a translation by Alison Dione Johnson. Greenwich: National Maritime Museum, Maritime Monographs and Reports, No. 52, 1982. Pp. vi + 222. ISBN 0-905555-60-0. No price given". The British Journal for the History of Science. 18 (1): 103–103. doi:10.1017/s0007087400021890. ISSN   0007-0874.
  10. "The Antiquarian Astronomer, June 2016 p. 38" (PDF).
  11. Yoder, Paul R. Jr. (2005). Opto-Mechanical System Design, Third Edition. CRC Press. p. 247. ISBN   1420027239.