In this article, we present Spar (simultaneous planner for assembly robots), an implemented system that reasons about high-level operational goals, geometric goals, and uncertainty-reduction goals to create task plans for an assembly robot. These plans contain manipulations to achieve the assembly goals and sensory operations to cope with uncertainties in the robot's environment. High-level goals (which we refer to as operational goals) are satisfied by adding operations to the plan using a nonlinear, constraint-posting method. Geometric goals are satisfied by placing constraints on the execution of these operations. If the geometric configuration of the world prevents this, Spar adds new operations to the plan along with the necessary set of constraints on the execution of these operations.