Original Research Article Proc IMechE Part C: J Mechanical Engineering Science 2021, Vol. 0(0) 1–13 © The Author(s) 2021 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/09544062211063432 journals.sagepub.com/home/pic Effect of novel continuous friction model on nonlinear dynamics of the mechanisms with clearance joint Amirhosein Javanfar and Mahdi Bamdad  Abstract A general methodology for the dynamic modelling and analysis of planar multi-body systems with a continuous friction model in joint clearance is presented. Joint clearance is the critical factor that influences the dynamic response and the performance of mechanisms for high-speed application. In light of recent developments in the joint clearance studies, the number of contact force models has been introduced with ignoring friction continuity. The selection of an appropriate continuous friction model is still challenging and essential, which requires further development. Therefore, a perfect continuous friction model, including the Stribeck effect, static, dynamic and viscous friction terms, is proposed and validated. Investigating the dynamic modelling and analysis of double rocker four-bar linkage mechanisms with frictional revolute clearance joints is presented to investigate friction models’ effect when surfaces collide with a non-zero tangential velocity. Unlike the smooth crank input mechanism, a double rocker four-bar linkage mechanism is analysed as a challenging problem in the impact mode. Resolving this concern, the novel friction model avoids discontinuity at zero velocity considering the accurate static friction zone. The results reveal that the novel friction model, compared with the piecewise friction model, is more effective in reflecting the mechanical systems’ dynamic behaviour. In order to grasp the nonlinear characteristics of the high-speed four-bar linkage mechanism with our model in joint clearance, the Poincar´ e portrait, and Fast Fourier transformation plot are employed. It is proved that chaos exists in the dynamic response with the influence of the restitution coefficients and kinetic coefficient of friction. Keywords Clearance, contact force, friction, nonlinear model, fast fourier transformation, bearing, multibody dynamics, four-bar linkage, impact Date received: 5 July 2021; accepted: 20 October 2021 Introduction In the dynamic analysis of mechanisms, there are some physical parameters involved that usually are not addressed in order to simplify analysis. This simplification leads to a notable mismatch between actual behaviour and numerical simulation result. One such parameter is the joint clearance that is usually caused by manufacturing and assembling tolerances. The existence of joint clearance leads to addi- tional degrees of freedom in the system, and the mechanism undergoes sudden impacts, causing undesirable vibrations, lower accuracy and chaotic dynamical behaviour. 1 The clearance joint in the high precision mechanisms and mechanical devices has attracted considerable attention, particularly in high-speed applications. 1–3 Clearance affects system dynamic performance and response ac- curacy as well as generation of vibration and noise. Therefore, the stability of the system must be analysed. Moreover, the researchers observed that the dynamic response of mechanisms with clearance joint is chaotic at relatively high crank speeds. 4,5 The vital issue of joint clearance modelling is contact model and friction model. Nonetheless, well-known Lankarani and Nikravesh approach (L-N) 6 is extensively employed with contact force models. 7 Also, Pereira et al. 8 developed an enhanced contact force model based on the Johnson contact model 9 to describe the interaction between the journal and bearing. Although the L-N model shows a little softer force-penetration relation, it is suitable for the joint clearance model. Hence, L-N model could be the most used contact model for clearance joints in the linkage mechanisms. Recently, contact models have been discussed in several kinds of research. For contact problems with complex geometries and energy dissipations, a continuous contact force model is presented. 10 The nonlinear stiffness of contact force varying with clearance and penetration is investigated within a contact collision model for the Mechanical and Mechatronics Engineering School, Shahrood University of Technology, Shahrood, Iran Corresponding author: Mahdi Bamdad, Mechanical and Mechatronics Engineering School, Shahrood University of Technology, Shahrood 3619995161, Iran. Email: bamdad@shahroodut.ac.ir