Natural molecular machines contain protein components that undergo motion relative to each other. Designing such mechanically constrained nanoscale protein architectures with internal degrees of freedom is an outstanding challenge for computational protein design. Here we explore the de novo construction of protein machinery from designed axle and rotor components with internal cyclic or dihedral symmetry. We find that the axle-rotor systems assemble in vitro and in vivo as designed. Using cryo-electron microscopy, we find that these systems populate conformationally variable relative orientations reflecting the symmetry of the coupled components and the computationally designed interface energy landscape. These mechanical systems with internal degrees of freedom are a step toward the design of genetically encodable nanomachines.