Allosteric mechanisms are fundamental to the operation of biomolecular motors. Recreating the molecular phenomena associated with allostery, from first principles, would help advance the design and construction of synthetic molecular motors, which remain quite simple compared natural motors. In this study, I present a model for generating allosteric interactions using mechanical linkages, which are devices in which flexible nodes are connected by rigid rods. I describe how allosteric information can be communicated between multivalent binding sites on an enzyme when linkages bind or dissociate in a stepwise fashion, which takes place stochastically according to assigned binding rates and partitioned binding energies. This design allows geometric competitions to autonomously push a linkage enzyme through a desired sequence of states, driven by consumption of a fuel. I use the model to emulate the chemical and conformational cycle of a myosin monomer, which is demonstrated by simulating chemical reaction networks of the linkage structures, and by describing how two linkage monomers can be connected together to construct a motor that walks on a track. This work shows how the complex behavior of biomolecular motors can be recapitulated with simple geometric and chemical principles that encode allosteric mechanisms. Because the concepts are material-agnostic, they can potentially be used to design and construct allosteric machines using various chemistries.