Complex robots with many degrees-of-freedom (e.g., humanoids, mobile manipulators) have been increasingly applied to achieve tasks in fields such as disaster relief or spacecraft logistics. Finding motions for these systems autonomously is necessary if they are to be applied in unstructured environments not known a priori, as they must compute motions on-the-fly. Sampling-based motion planning algorithms have been shown to be effective for finding motions for high-dimensional systems such as these. However, the problems these robots face typically take the form of tasks with constraints, which limit the valid motions a robot can take (e.g., turning a valve about its axis, carrying a tray with both arms, etc.). Incorporating constraints while planning introduces significant challenges, as constraints induce a lower-dimensional manifold of constraint-satisfying configurations within the robot’s configuration space. The lower-dimensional structure of the manifold throws a wrench into the basic operation of a sampling-based planner, necessitating a constraint methodology to provide a means for the planner to satisfy constraints. Within the literature, many constrained sampling-based motion planning methods have been proposed for sampling-based planning with constraints. Each of these methods introduces a constraint methodology of their own to tackle the issues raised when considering constraints. This thesis organizes the menagerie of constraint methodologies along of a spectrum, cataloged by the amount of bookkeeping and computation used to approximate the manifold of constraint-satisfying configurations. Notably, previous constrained sampling-based methods augment a single sampling-based algorithm with their constraint methodology to create a bespoke planner. This thesis presents a general framework for sampling-based motion planning with geometric constraints, unifying prior works by approaching the constrained motion planning problem at a higher level of abstraction. The framework decouples the constraint methodology from the planner’s method for exploration by presenting the constraint-induced manifold as a configuration space to the planner, hiding details of the constraint methodology behind the space’s primitive operations. Three constraint methodologies from the literature are emulated within the framework. The framework is demonstrated with a range of planners using the three emulated constraint methodologies in a set of simulated problems. Results show the advantages decoupling brings to constrained sampling-based planning, with novel combinations of planners and constraint methodologies surpassing emulated prior works. The framework is also easily extended for novel planners and constraint spaces.