This study presents an analytical-mathematical model that elucidates the mechanics/kinematics of an impact crusher’s impact swing mechanism. Essentially, this model comprises a series of mathematical descriptions and equations that are leveraged from established mechanical principles, such as rigid body kinematics, multibody dynamics, and collision laws, thus enabling comprehensive analytical exploration of the complex mechanical-kinematical system underlying the impact swing’s mechanism, particularly focusing on the system-critical activation of this mechanism when triggered by an impacting non-fragile particle. The developments presented in this paper, supportively illustrated through detailed diagrams, provide relevant insights into the operational behaviour of modern impact crushers. This research therefore not only advances the theoretical understanding of system-critical crusher kinematics but also holds significant implications for the design and optimisation of future equipment. The resulting model’s ability to analytically and mathematically delineate the complex mechanical-kinematical system of an impact swing mechanism not only facilitates efficient analyses but also circumvents the extensive and resource-intensive demands typically associated with numerical simulations of such systems. Consequently, this approach thereby forms substantial added value, particularly in the realm of engineering analysis.