This study consists of research on developmental processes, fundamentals, kinematic properties, and design methods of art and architectural examples that involve mechanisms and a proposal of a novel method of designing polygonal deployable surfaces. The effect of motion studies on art and architecture is analyzed from the first technical studies of motion and portable examples of architecture. The pre-industrial automata, acoustic designs, musical instruments, water-lifting devices, and aqueducts were designed by artists and architects as well; windmills that are the first rotating structures, clocks, clock towers, construction machines and early examples of movable bridges are examined. The kinematic properties and fundamentals of mechanisms are analyzed. The kinematic structural analyses of contemporary art and architectural products are conducted by drawing kinematic diagrams, demonstrating link and joint types and numbers; and mobility calculations. The primary units and assembly methods of them are examined. Strengthening the bond among the fields of kinetic architecture, art and mechanism science is intended. The present study is the first source in which examples from the related fields and corresponding kinematic science are explicitly transmitted for artists and architects. Finally, a novel design method for polygonal deployable surfaces that is adaptable to climatic, functional, visual and/or social needs is developed. The method starts with the kinematic design of the triangular primary unit, which is topologically Bennett's plano-spherical mechanism. The planar position provides covering surfaces, while the spherical linkage generates a 3D dynamic form during movement. The design is adapted to polygons and multiplied in Archimedean tilings. A single actuator can drive all designs. The modularity provides designs versatility and flexibility.