<p>Humans instinctively use both pushing and wiggling motions when inserting objects into sockets, connectors, or mechanical interfaces that resist fitting, often without understanding the rationale behind these actions. Despite their apparent simplicity, such tasks involve complex mechanical interactions that are challenging to describe mathematically. In this paper, we present a simplified two-leg mathematical model that clarifies the fundamental principles governing the combined pushing-wiggling during assembly. The model integrates forces, moments, frictional reactions, and other uncertain effects into several effective factors representing overall mechanical behavior, classifying the relationship between these factors and connector movements into nine cases and demonstrating that the coordinated application of force and moment facilitates insertion. The experimental validation confirms the effectiveness of the model and highlights the role of wiggling in overcoming insertion resistance. Moreover, the model successfully generalizes across various connector types, pin counts, and configurations, offering insights into the broader mechanics of human-inspired insertion strategies.</p>