We consider a molecule constrained to a hypersurface S
in the conguration space Rm.
In order to derive an expression for the mean force
acting along the constrained coordinate
we decompose the molecular vector field,
and single out the direction of the respective coordinate
utilising the structure of affine connections.
By these means we reconsider the well-known results derived by Sprik et al. [1]
and Darve et al. [2];
we gain concise geometrical insight into the different contributions
to the force in terms of molecular potential, mean curvature,
and the connection 1-form of the normal bundle over the submanifold S.
Our approach gives rise to a Hybrid Monte-Carlo based algorithm
that can be used to compute the averaged force acting on selected coordinates
in the context of thermodynamic free energy statistics.