In the design of a machine, some of the dimensions are easily determined by the geometric requirements of the task to be performed. The parts must be large enough to reach from point to point, they must be long enough to reach the required locations, and similar geometric considerations. But there is the ever present question as to how thick the members must be in order to carry the required loads, and this is a question for which there is no a priori answer. The answer is always, big enough, but how big is that? The only way to determine what is big enough is to determine what the loads (forces) are. As well as sizing the members themselves, there is the related matter of sizing the bearings of the machine.
In a static structure, the determination of the loads is simply a matter of a static force analysis. With a machine, where things move and the configuration of the components changes as the machine moves through a cycle, there are two complicating factors involved in the force analysis:
(1) the changing geometry means that the forces must be analyzed as functions of position;
(2) the inertial effects of the machine components enter into the dynamics of the system, affecting the force analysis.
Item (1) implies that the forces must typically analyzed at many different positions, with the understanding that they are expected to vary continuously between positions. Item (2) means that Newton’s Second Law, rather than the equations of statics govern the force relations. It also implies that a kinematic analysis through the accelerations will have to precede the force analysis in order to express the accelerations for the various components.
With very few exceptions, the typical machine is a single degree of freedom device. For that reason, the discussion to follow is limited to SDOF machines
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