Abstract
Connecting joints are significant components in mechanical systems as well as the Cartesian flexible robotic manipulator (FRM) which consists of a flexible arm and a moving base through connecting joints. Uncertain factors, such as unqualified assembly, accidental collision, and longtime service, will reduce the restraint stiffness of the connecting joints and enhance the dynamic nonlinearity of the system subsequently. In this case, the traditional perfectly fixed restrained model cannot reflect the real property of the connecting joints. This paper focuses on the elasticity property of the connecting joints with uncertain restraint stiffness, which is defined as the elastically restrained connecting joints (ERCJ), and investigates the dynamic characteristics and restraint mechanism of the ERCJ. An elastic restrained model is proposed to describe the elasticity property of the connecting joints and determine the elastic restrained region of the ERCJ, and the frequency relationship equation in the elastic restrained region is simultaneously determined and verified. Based on the proposed elastic restrained model and Hamilton’s variational principle, the dynamic model and vibration displacement equation of the FRM with elastically restrained connecting joints (FRMERCJ) are established. The virtual prototype experiment of the FRMERCJ is conducted to verify the dynamic model and reveal the restraint mechanism of the ERCJ. The proposed elastic restrained model in this paper can accurately describe the elasticity property of the connecting joints, and the ERCJ is sensitive to motion velocities especially under higher velocities for higher-order vibrations in the initial stage. The results are meaningful for the dynamic analysis and vibration control of robotic manipulators.
Highlights
Flexible manipulators have gradually applied in robotic systems [1,2,3]
A Cartesian flexible robotic manipulator (FRM) can be modeled as a moving base, a flexible arm, and an end effector, which remains a typical rigid-flexible coupling system conveying rigid motions of the moving base and elastic vibrations of the flexible arm. is rigid-flexible coupling effect is transmitted through the connecting joints between the moving base and the flexible arm, for example, the bolted joints which are frequently used in mechanical systems and the Cartesian robotic systems because of their simple configuration, convenient operation, and low cost [7, 8]. Due to their flexibility properties, FRMs will be more sensitive to this rigid-flexible coupling effect [9]. erefore, the dynamic characteristic and effect of the connecting joints should be considered in the investigations of FRMs, especially for the accurate dynamic analysis and vibration control
Lu et al [13] proposed a composite control of a rotational FRM with trajectory tracking of the driving system and vibration suppression of the exible arm. e exible arms in these indicated investigations are commonly installed on the moving base through bolted joints, and the bolted joints in the dynamic model are regarded as absolutely xed restrained joints without considering the elastic or exible property of the connecting joints, which is di cult to achieve in actual applications
Summary
Flexible manipulators have gradually applied in robotic systems [1,2,3]. Compared with rigid robotic manipulators (RRMs) constructed with heavy materials and bulky structures, flexible robotic manipulators (FRMs) are more lightweight and flexible and have been widely applied in aeronautics, astronautics, and precision manufacturing [4,5,6]. Is rigid-flexible coupling effect is transmitted through the connecting joints between the moving base and the flexible arm, for example, the bolted joints which are frequently used in mechanical systems and the Cartesian robotic systems because of their simple configuration, convenient operation, and low cost [7, 8]. Due to their flexibility properties, FRMs will be more sensitive to this rigid-flexible coupling effect [9]. In this paper, aiming at the connecting joints between the exible arm and the moving base and considering their elasticity property, an accurate dynamic model will be established to investigate the coupling dynamic characteristics of the FRM system.
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