We have recently proposed a new unified theoretical scheme (the "middle" scheme) for thermostat algorithms for efficient and accurate configurational sampling of the canonical ensemble. In this paper, we extend the "middle" scheme to molecular dynamics algorithms for configurational sampling in systems subject to constraints. Holonomic constraints and iso-kinetic constraints are used for demonstration. Numerical examples indicate that the "middle" scheme presents a promising approach to calculate configuration-dependent thermodynamic properties and their thermal fluctuations.