Consider a joint between two rigid bodies. Each rigid body has m degrees of freedom (m=3 for a planar rigid body and m=6 for a spatial rigid body) in the absence of any constraints. The joint has f degrees of freedom (e.g., f=1 for a revolute joint or f=3 for a spherical joint). How many constraints does the joint place on the motion of one rigid body relative to the other? Write your answer as a mathematical expression in terms of m and f.
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In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations, and other aspects of logical syntax.
Many authors distinguish an expression from a formula, the former denoting a mathematical object, and the latter denoting a statement about mathematical objects.[citation needed] For example, {\displaystyle 8x-5} 8x-5 is an expression, while {\displaystyle 8x-5\geq 5x-8} {\displaystyle 8x-5\geq 5x-8} is a formula. However, in modern mathematics, and in particular in computer algebra, formulas are viewed as expressions that can be evaluated to true or false, depending on the values that are given to the variables occurring in the expressions. For example {\displaystyle 8x-5\geq 5x-8} {\displaystyle 8x-5\geq 5x-8} takes the value false if x is given a value less than –1, and the value true otherwise.