Idle Degrees of Freedom and Equivalent Mechanisms in the Study Topic of Structural Analysis

The manuscript discusses two controversial issues that are highly inherent to teaching/learning Machine and Mechanism Science (MMS). On one hand, students should be taught to be broad-minded about alternative structures of mechanisms and given opportunities to get rich experience with different means of providing assigned output motion, transformations, and inversions. Reflection of this kind is required for future designer of mechanisms and machines. On the other hand, to be creative, one should be based on frameworks, rules, techniques. Classic MMS textbooks provide solid foundation, vast compendiums of relevant knowledge. Although some topics are often explained with sample examples, not enough attention is paid to formulating rules. Rules are very important for junior MMS learners. This manuscript touches upon stating rules in two topics of structural analysis the first part of MMS study course. The identification of idle degrees of freedom (DOF) of a mechanism is reduced to five distinctive cases. The issue of transformation of mechanism structure and establishing equivalent linkages is discussed in such a way to answer questions: why, how, and what to do with the results. For a geared linkage a technique of making equivalent linkage is obtained. The manuscript argues that this mechanism has an isomorphic structure with link lengths not depending on the position, hence its kinematics can be discovered numerically. This gives students an example of thorough analysis within one of primary topics in MMS study course.