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Clearances are necessary in assemblage of mechanisms to allow the relative motion between the members. This clearance is due to machining tolerances, wear, material deformations, and imperfections, and it can worsen mechanism performance such as precision and vibration. As a new study in this topic, the effect of joint stiffness on the variation of instantaneous natural frequencies and mode shapes of a flexible four-bar mechanism with a clearance between coupler and follower is studied in this paper. To model the clearance, the continuous contact approach is used. The Lankarani's and Nikravesh's continuous contact force model is used to model the contact force arising from contact between journal and bearing. Finite element method is used to determine the instantaneous natural frequencies and their corresponding mode shapes. The stiffness of the clearance is modeled as a linear spring added to the assembled stiffness matrix. To validate the clearance model in rigid mechanism, the dynamic response is compared with the results in the literature. To show the validity of the formulation which calculates the instantaneous natural frequencies, two methods are used and compared with each other in the case no clearance exists. The results show that taking the joint stiffness into account has a considerable effect on the instantaneous natural frequencies and their corresponding mode shapes of a flexible multibody system.

Purpose The purpose of this paper is to investigate the effect of joint clearance on the behavior of a needle driver mechanism (a slider-crank linkage) of a typical sewing machine with an imperfect joint between the coupler and the slider (including needle). Design/methodology/approach In order to model the clearance, the momentum exchange approach is used. The Lankarani and Nikravesh’s continuous contact force model is used to model the contact force, and the modified Coulomb’s friction law represents the friction between sliding members. The penetration force applied on the needle by fabric is chosen based on an experimental data in the literature. The dynamic response is validated for the existing properties in the literature without considering the penetration force. Findings It is shown that the clearance joint made considerable effect on the dynamic response of the system. The rough changes of the needle acceleration and jerk are obvious. The base reaction force changed roughly and did not vary as smooth as that of the mechanism with ideal joint. So, clearance joint in the mechanism could lead to an undesirable vibration in the system. Furthermore, the crank driver must provide a non-smooth moment on the crank to keep the crank rotational velocity constant. Moreover, reducing the clearance size sufficiently could make the dynamic response closer to that of the mechanism with ideal joint. In addition, smoother crank moment could be required if the clearance size is reduced sufficiently. Furthermore, the rough change of the base reaction force which can represent the vibration caused by the mechanism on the fixed frame could be reduced if the clearance size is small enough. Originality/value Lockstitch sewing machine is one of the most common apparel industrial machines. The needle driver mechanism of a sewing machine could have an important role for proper stitch forming. On the other hand, clearances are inevitable in assemblage of mechanisms to allow the relative motion between the members. This clearance is due to machining tolerances, wear, material deformations, and imperfections, and it can worsen mechanism performance such as precision, dynamic behavior and vibration. Unfortunately, despite the importance of the dynamic behavior of the needle driver mechanism from practical point of view, very little publications have focused especially on the investigation of the effect of clearance joint on the dynamic behavior of the sewing machine which could lead to undesired vibration of the system and shorter lifetime as a result. In this paper, the dynamic behavior of the system including, needle velocity and acceleration, crank moment and base reaction force was compared with that of the ideal mechanism. Finally, the effect of clearance size on the dynamic behavior of the system was investigated.