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This paper proposes a methodology to calculate both the first and secondderivatives of a vector function of one variable in a single computation step.The method is based on the nested application of the dual number approach forfirst order derivatives.  It has been implemented in Fortran language, a module which contains the dualversion of elementary functions as well as more complex functions, which arecommon in the field of rotational kinematics. Since we have three quantities ofinterest, namely the function itself and its first and second derivative, ourbasic numerical entity has three elements. Then, for a given vector function$f:\mathbb{R}\to \mathbb{R}^m$, its dual version will have the form$\tilde{f}:\mathbb{R}^3\to \mathbb{R}^{3m}$.  As a study case, the proposed methodology is used to calculate the velocityand acceleration of a point moving on the coupler-point curve generated by aspherical four-bar mechanism.

A Dual Number Approach for Numerical Calculation of Velocity and Acceleration in the Spherical 4R Mechanism