Kinetostatic Analysis of the Propulsion System for a Mobile in-pipe Inspection Robot

Problem statement. The structural integrity of extensive pipeline networks is critical for economic and environmental safety, demanding reliable inspection methods. Mobile In-Pipe Inspection Robots (IPIRs) offer a non- disruptive solution; however, the design of their propulsion systems for confined and complex environments remains challenging. Existing analytical frameworks often exhibit a disconnect between kinematic modeling (motion planning) and force analysis (stability and traction), particularly for advanced hybrid locomotion strategies. This gap hinders the systematic optimization and control of IPIR designs. Purpose. This research aims to develop and analyze a comprehensive kinetostatic model for the propulsion system of a specific IPIR design: a two-module robot utilizing an inchworm locomotion strategy, driven by an internal slider-crank mechanism and rectified by overrunning clutches. The goal is to establish a mathematical model that accurately links the kinematics of motion with the forces required to execute it. Methodology. The study employs a kinetostatic analysis based on the Lagrangian approach. The robot is conceptualized as a hybrid dynamic system operating in two distinct modes: expansion and contraction. The crank rotation angle is adopted as the generalized coordinate. Equations of motion are derived for each mode, accounting for the constraints imposed by the ideal overrunning clutches, which enforce unidirectional movement. The resulting stiff and non-smooth differential equations are implemented in Wolfram Mathematica and solved numerically using the ‘StiffnessSwitching’ method to handle the discontinuous dynamics accurately. Results. The numerical simulation successfully validates the inchworm locomotion principle, demonstrating the characteristic alternating movement of the modules. Under a constant driving torque (0.25 N‧m), the robot exhibits continuous acceleration, with peak velocities approaching 4 m/s within the first second. Analysis of the velocity profiles confirms the non-overlapping nature of the module movements, validating the idealized clutch model. A key finding is the presence of extremely large acceleration spikes occurring instantaneously at the transitions between expansion and contraction modes, highlighting significant dynamic impacts inherent in this locomotion strategy. Novelty. The novelty lies in the rigorous derivation of a kinetostatic framework specifically tailored to an inchworm IPIR with overrunning clutches. By applying Lagrangian mechanics to this hybrid dynamic system, the study provides a unified analytical foundation that bridges the gap between motion generation and force analysis for this class of robots. Practical value. The developed mathematical model serves as a powerful tool for optimizing the design parameters (e. g., mass distribution, linkage geometry, actuator sizing) of inchworm IPIRs. It provides critical insights into the system’s dynamic behavior, particularly emphasizing the need to mitigate the high dynamic loads generated during clutch engagement in practical imple- mentations. Scope of further investigations. Future research should focus on refining the model to incorporate non- ideal clutch behaviors (e.g., compliance and friction dynamics), analyzing locomotion in complex geometries (bends and vertical sections), and developing model-based control strategies.