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  2. Product of exponentials formula - Wikipedia

    en.wikipedia.org/.../Product_of_exponentials_formula

    For each joint of the kinematic chain, an origin point q and an axis of action are selected for the zero configuration, using the coordinate frame of the base. In the case of a prismatic joint, the axis of action v is the vector along which the joint extends; in the case of a revolute joint, the axis of action ω the vector normal to the rotation.

  3. Formulas for generating Pythagorean triples - Wikipedia

    en.wikipedia.org/wiki/Formulas_for_generating...

    from the formula for the tangent of the difference of angles. Using s instead of r in the above formulas will give the same primitive Pythagorean triple but with a and b swapped. Note that r and s can be reconstructed from a , b , and c using r = a / ( b + c ) and s = b / ( a + c ) .

  4. Pairwise independence - Wikipedia

    en.wikipedia.org/wiki/Pairwise_independence

    Pairwise independence does not imply mutual independence, as shown by the following example attributed to S. Bernstein. [3]Suppose X and Y are two independent tosses of a fair coin, where we designate 1 for heads and 0 for tails.

  5. Best arthritis pain relief cream of 2024, according to experts

    www.aol.com/lifestyle/arthritis-pain-relief...

    Penetrex's Warming Pain Relief Cream is a vegan formula that aids in soothing muscle and joint pain with the use of capsaicin, arnica and MSM. Capsaicin has been shown to reduce pain signals ...

  6. Adjoint functors - Wikipedia

    en.wikipedia.org/wiki/Adjoint_functors

    Dually, the triple 〈FG, ε, FηG〉 defines a comonad in C. Every monad arises from some adjunction—in fact, typically from many adjunctions—in the above fashion. Two constructions, called the category of Eilenberg–Moore algebras and the Kleisli category are two extremal solutions to the problem of constructing an adjunction that gives ...

  7. Slider-crank linkage - Wikipedia

    en.wikipedia.org/wiki/Slider-crank_linkage

    This inverted slider-crank is the form of a slider-crank linkage that is often used to actuate a hinged joint in construction equipment like a crane or backhoe, as well as to open and close a swinging gate or door. [2] [3] [4] A slider-crank is a four-bar linkage that has a crank that rotates coupled to a slider that the moves along a straight ...

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