Summary: Two traditionally separate fields, the statics of bar and joint frameworks and the instantaneous kinematics of articulated panel structures, are here united in a novel and appropriate projective geometric setting. We employ exterior algebra (or Cayley algebra) to represent equilibrium loads and static stresses on a bar and joint framework, and to represent instantaneous motions of an articulated panel structure. In the special case of a framework and a panel structure, one built on the edge skeleton, the other on the face structure, of a spherical polyhedron, we exhibit a natural algebraic isomorphism between static stresses in the framework and instantaneous motions of the panel structure. Under a suitable path condition on the stresses, we extend this isomorphism to frameworks and panel structures based on arbitrary oriented polyhedra.