ABSTRACT
This chapter serves as a text for a course using dual-number methods as well as a manual for the reader to develop his or her abilities for the design of machinery or evaluation of mechanical systems. "Equilibrium" is defined as a state where the resultant force on a particle vanishes. A rigid body is in equilibrium if each of its constituent particles is in equilibrium, and a system is in equilibrium if each of its constituent rigid bodies is in equilibrium. A rigid body is in equilibrium if the summation of all the external dual forces applied on the rigid body, considered at the same point and in the same frame, vanishes. A mechanism is considered to be a system in static equilibrium if each of its links is held stationary by a set of applied dual forces. Under static conditions and in the absence of friction, an intermediate revolute joint cannot support a torque about its axis.
