This paper focuses on the reconfiguration analysis of three multi-mode single-loop 6R spatial mechanisms, each consisting of six revolute (R) joints. Initially, the construction of these mechanisms is established. Subsequently, reconfiguration analysis is carried out in the configuration space by solving a set of kinematic loop equations. This is accomplished using dual quaternions and substituting the natural exponential function, employing tools from algebraic geometry. The analysis reveals that the three multi-mode single-loop 6R spatial mechanisms exhibit differing numbers of motion modes: six, four, and four respectively. These modes include rotational 1R modes, double Bennett 6R modes, parallelogram 4R modes, plane symmetry 6R modes, and anti-parallelogram 4R modes. Importantly, it is demonstrated that modifying the link parameters of a mechanism can induce changes in its motion modes.