Elastodynamic modeling of hybrid serial–parallel robots accounting for nonlinear effects

Purpose Elastodynamic analysis is crucial for characterizing the dynamic behavior and elastic positioning errors of robotic systems. In this study, an elastodynamic model of a hybrid serial–parallel robot is developed using the finite element method and Lagrange’s equations, explicitly accounting for geometric nonlinearity and nonuniform element properties. Solving this model enables accurate prediction of the robot’s load-induced elastic deformations and dynamic characteristics throughout its motion. Design/methodology/approach This paper partitions each branch into multiple spatial flexible beam elements, formulates kinetic and deformation energy expressions that incorporate nonlinearities and derives the element-level elastodynamic equations via Lagrange’s equations. Accounting for inter-element relationships, the element equations are assembled into a branch-level elastodynamic model. By enforcing the system’s kinematic and dynamic constraints, the branch-level models are further assembled into the elastodynamic model of the parallel mechanism. Subsequent analysis of the serial section completes the assembly, yielding an integrated elastodynamic model. Findings Based on the solutions of the elastodynamic model implemented in MATLAB, it is shown that, along the prescribed –trajectory and with nonlinear effects taken into account, the maximum elastic deflections of the tool tip under 100 N loads applied in the x-, y- and z-directions (including self-weight) are 4.43, 3.74 and 2.31 mm, respectively. In addition, hammer-impact tests were conducted to obtain the frequency response functions (FRFs) and natural frequencies of the tool tip at different robot postures. Comparison between the experimental results and the theoretical predictions demonstrates very good agreement in both the frequency-domain responses and the identified modes, thereby validating the accuracy of the proposed elastodynamic modelling approach. Practical implications The proposed model can be integrated into robot controllers and offline programming to predict posture-dependent FRFs and load-induced deflection, enabling resonance avoidance and error compensation. This can shorten commissioning time, reduce scrap and improve competitiveness in high-precision machining. Social implications By improving machining accuracy and stability, the work helps reduce rework and material waste, lowers energy consumption and vibration/noise risks and supports higher manufacturing quality and reliability in critical sectors such as aerospace. Originality/value This modeling approach fully accounts for the constraint conditions within each limb and the inter-limb coupling constraints, while incorporating geometric nonlinearity. As a result, it improves the predictive accuracy of time-varying, load-induced elastic deformations and the associated configuration (posture)-dependent dynamic characteristics. These enhancements are directly relevant to robotic machining, providing a quantitative basis for avoiding resonance-prone spindle-speed ranges, enabling posture-aware process parameter selection and compensating load-induced deflections to reduce dimensional and surface errors.