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In this article, we show that the principle of superposition can be applied for analyzing the spatial motion of a bevel geared three‐roll wrist with nonzero oblique angle. The total motion of the wrist is decomposed into three independent component motions, which are easier to analyze. A superposition tabulation is then constructed to derive the relations among the three wrist joint variables and three coaxial actuation variables. The displacement solution for the wrist joint variables is found by using the zero reference position method.

Signal flow graphs (SFG) have been applied in many areas such as circuit analysis, controls, mechanical vibrations, statistics, and operations research. They have also been applied to the analysis of planetary gear trains which are planar, i.e., where all of the gear axes are parallel. In this paper, signal flow graphs are applied to spatial planetary gear trains. Some additional terminology and rules which are needed for this important application are developed in this paper and illustrated by examples. The significance of applying SFG to a gear system is that the graph describes the interrelationship among the system variables by linking causes and effects, offers the information about the topology of system connection, and the kinematic equations of motion can be written easily by inspection. In this way, it helps use to visualize and understand spatial gear train systems better.

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