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astronomy

Universal joint

Universal joint is a astronomy topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Universal joint rather than just read about it. In short: A universal joint (also called a universal coupling or U-joint) is a joint or coupling connecting rigid shafts whose axes are inclined to each other. It is commonly used in shafts that transmit rotary motion.

Universal joint — main illustration
Universal joint — illustration

Key takeaways

  • Universal joint belongs to astronomy; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Universal joint to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Universal joint from memory before moving on to harder problems.

Reference excerpt

A universal joint (also called a universal coupling or U-joint) is a joint or coupling connecting rigid shafts whose axes are inclined to each other. It is commonly used in shafts that transmit rotary motion. It consists of a pair of hinges located close together, oriented at 90° to each other, connected by a cross shaft. The universal joint is not a constant-velocity joint. U-joints are also sometimes called by various eponymous names, as follows:

Cardan joint, after Gerolamo Cardano, a polymath of the 16th century who contributed to knowledge of various clever mechanisms, including gimbals Hooke joint or Hooke's joint, after Robert Hooke, a polymath of the 17th century who contributed to knowledge of various clever mechanisms Spicer joint, after Clarence W. Spicer and the Spicer Manufacturing Company, who manufactured U joints Hardy Spicer joint, after the Hardy Spicer brand, a successor to the Spicer brand

History

The main concept of the universal joint is based on the design of gimbals, which have been in use since antiquity. One anticipation of the universal joint was its use by the ancient Greeks on ballistae. In Europe the universal joint is often called the Cardano joint (and a drive shaft that uses the joints, a Cardan shaft), after the 16th century Italian mathematician, Gerolamo Cardano, who was an early writer on gimbals, although his writings mentioned only gimbal mountings, not universal joints. The mechanism was later described in Technica curiosa sive mirabilia artis (1664) by Gaspar Schott, who mistakenly claimed that it was a constant-velocity joint. Shortly afterward, between 1667 and 1675, Robert Hooke analysed the joint and found that its speed of rotation was nonuniform, but that property could be used to track the motion of the shadow on the face of a sundial. In fact, the component of the equation of time which accounts for the tilt of the equatorial plane relative to the ecliptic is entirely analogous to the mathematical description of the universal joint. The first recorded use of the term 'universal joint' for this device was by Hooke in 1676, in his book Helioscopes. He published a description in 1678, resulting in the use of the term Hooke's joint in the English-speaking world. In 1683, Hooke proposed a solution to the nonuniform rotary speed of the universal joint: a pair of Hooke's joints 90° out of phase at either end of an intermediate shaft, an arrangement that is now known as a type of constant-velocity joint. Christopher Polhem of Sweden later re-invented the universal joint, giving rise to the name Polhemsknut ("Polhem knot") in Swedish. In 1841, the English scientist Robert Willis analyzed the motion of the universal joint. By 1845, the French engineer and mathematician Jean-Victor Poncelet had analyzed the movement of the universal joint using spherical trigonometry. The term universal joint was used in the 18th century and was in common use in the 19th century. Edmund Morewood's 1844 patent for a metal coating machine called for a universal joint, by that name, to accommodate small alignment errors between the engine and rolling mill shafts. Ephriam Shay's locomotive patent of 1881, for example, used double universal joints in the locomotive's drive shaft. Charles Amidon used a much smaller universal joint in his bit-brace patented 1884. Beauchamp Tower's spherical, rotary, high speed steam engine used an adaptation of the universal joint c. 1885. The term 'Cardan joint' appears to be a latecomer to the English language. Many early uses in the 19th century appear in translations from French or are strongly influenced by French usage. Examples include an 1868 report on the Exposition Universelle of 1867 and an article on the dynamometer translated from French in 1881. In the 20th century, Clarence W. Spicer and the Spicer Manufacturing Company, as well as the Hardy Spicer successor brand, helped further popularize universal joints in the automotive, farm equipment, heavy equipment, and industrial machinery industries.

Equation of motion

The Cardan joint suffers from one major problem: even when the input drive shaft axle rotates at a constant speed, the output drive shaft axle rotates at a variable speed, thus causing vibration and wear. The variation in the speed of the driven shaft depends on the configuration of the joint, which is specified by three variables:

γ 1 {\displaystyle \gamma _{1}} the angle of rotation for axle 1

γ 2 {\displaystyle \gamma _{2}} the angle of rotation for axle 2

… excerpt ends here. Continue reading the full article.

Illustrations

Universal joint: A universal joint
A universal joint
Universal joint: Spicer universal joints for motor cars, 1916.
Spicer universal joints for motor cars, 1916.
Universal joint: Diagram of variables for the universal joint. Axle 1 is perpendicular to the red plane and axle 2 is perpendicular to the blue plane at all times. These planes are at an angle β with respect to each other. The angular displacement (rotational position) of each axle is given by γ 1 {\displaystyle \gamma _{1}} and γ 2 {\displaystyle \gamma _{2}} respectively, which are the angles of the unit vectors x ^ 1 {\displaystyle {\hat {x}}_{1}} and x ^ 2 {\displaystyle {\hat {x}}_{2}} with respect to their initial positions along the x and y axis. The x ^ 1 {\displaystyle {\hat {x}}_{1}} and x ^ 2 {\displaystyle {\hat {x}}_{2}} vectors are fixed by the gimbal connecting the two axles and so are constrained to remain perpendicular to each other at all times.
Diagram of variables for the universal joint. Axle 1 is perpendicular to the red plane and axle 2 is perpendicular to the blue plane at all times. These planes are at an angle β with respect to each other. The angular displacement (rotational position) of each axle is given by γ 1 {\displaystyle \gamma _{1}} and γ 2 {\displaystyle \gamma _{2}} respectively, which are the angles of the unit vectors x ^ 1 {\displaystyle {\hat {x}}_{1}} and x ^ 2 {\displaystyle {\hat {x}}_{2}} with respect to their initial positions along the x and y axis. The x ^ 1 {\displaystyle {\hat {x}}_{1}} and x ^ 2 {\displaystyle {\hat {x}}_{2}} vectors are fixed by the gimbal connecting the two axles and so are constrained to remain perpendicular to each other at all times.
Universal joint: A sample universal joint colour-coded to the diagrams about the equation of motion. The red and blue planes are visible.
A sample universal joint colour-coded to the diagrams about the equation of motion. The red and blue planes are visible.
Universal joint illustration

Worked examples

Example 1 — a first encounter with Universal joint

Start with the simplest possible case. Write down what Universal joint claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Universal joint before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Universal joint ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Universal joint

In research
Universal joint appears in astronomy research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Universal joint in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Universal joint is common in secondary-school and first-year university syllabi. It links to neighbouring topics Automotive transmission technologies, Mechanisms (engineering), Rotating shaft couplings, so understanding it makes those chapters shorter.
In everyday life
Look for Universal joint outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Universal joint in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Universal joint means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Universal joint out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Universal joint in simple terms?

A universal joint (also called a universal coupling or U-joint) is a joint or coupling connecting rigid shafts whose axes are inclined to each other. It is commonly used in shafts that transmit rotary motion.

Why does Universal joint matter?

Because it connects several astronomy ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Universal joint?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Universal joint.

Tags

  • Automotive transmission technologies
  • Mechanisms (engineering)
  • Rotating shaft couplings

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