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When to use either expression?

Two Degree of Freedom System or Two Degrees of Freedom System?

For example, let's say you're in a class, the teacher came said:

Today we will discuss the kinematic model of a two degree of freedom robotic arm.

Would it be fine, or he should use:

...the kinematic model of a two degrees of freedom robotic arm.

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  • As written, it seems like these could be the proper names of two systems. As such, it could be either one. But in general it would be odd to use singular "degree" with "two". – user3169 Jan 28 '16 at 6:05
  • Could anyone who answers this question please also add why phrases like "three speed bicycle", "five year plan" or "five point method" are okay, even if this one isn't? (I don't think it is, but I don't really know why.) – modulusshift Jan 28 '16 at 6:05
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    @modulusshift For example, "three speed" is a descriptor of a type of bicycle. It is not about how many speeds there are. – user3169 Jan 28 '16 at 6:08
  • @modulusshift I've addressed your question in my answer below. – Lawrence Aug 25 '16 at 14:34
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A system with two degrees of freedom.

A system with two-degree freedom.

A rubber-band with four inches of stretch.

A rubber-band with four-inch stretch.

If the measurement element is singular (four-inch) it is an adjective that modifies the noun directly: four-inch stretch.

If the measurement element is a plural noun, (four inches), then it must be complemented by a prepositional phrase: four inches of stretch.

The second question is whether such a phrase is better before or after another noun which it modifies:

AFTER:
A robotic arm with two degrees of freedom.

A robotic arm with two-degree freedom.

BEFORE:
A two-degrees-of-freedom robotic arm.

A two-degree-freedom robotic arm.

It is better to place such a modifying phrase after the noun, connected to the noun using the preposition "with":

A robotic arm with two degrees of freedom.

A robotic arm with two-degree freedom.

In this usage, "with" means that the preceding noun-phrase ("a robotic arm") has the characteristic "two degrees of freedom".

A synonym for "with" in this usage would be having:

A robotic arm having two degrees of freedom.
A robotic arm having two-degree freedom.

In my opinion, "with" is simpler and therefore better than "having".

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From English Channel:

Number Modifier When a number (greater than one) modifies a noun, the noun is plural.

  • The ladder had six steps.
  • The book has 200 pages.

Number + Noun Modifier When a number and noun are combined to modify a noun, no plural form is used in the modifier. Adjectives do not take the plural form.

  • It was a six-step ladder.
  • It was a two-hundred-page book.

Your example uses the second form, so it should be:

  • Today we will discuss the kinematic model of a two-degree-of-freedom robotic arm.

This form is also used for Number + Noun Modifier expressions like "three-speed bicycle", "five-year plan" and "five-point method". Note that the adjectival phrase is hyphenated because it is a compound adjective with a leading number.

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