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This work analyzes various designs of multi-link linkage mechanisms with rotational kinematic pairs in the form of cylindrical joints of high load capacity that are widely used in various fields of technology. The use of multiple joints in such linkage mechanisms simplifies their design, reduces dimensions, weight and cost, as well as expands their functionality and the range of movement of the working body. The considered methodology of the system analysis of the structure and mobility of plane multi-loop linkage mechanisms with multiple joints includes the sequential determination of all the basic topological characteristics of the closed kinematic chain of a complex mechanism and its mobility in a given space of possible movements from a set of simple algebraic equations. The effectiveness of the proposed method for constructing reliable mechanisms with any given number and type of multi-loop joints is confirmed by the presented examples of the system analysis of the structure and mobility of plane multiple lever mechanisms used in various fields of modern engineering.