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Featured Application: (1) Static stiffness modelling methods are classified and summarized. Each method is studied with regards to algorithms, implementation, and limitations; (2) A single degree of freedom and multiple degrees of freedom are proposed to describe the modelling methods in the joint space. (3) Regarding the relationship between external force and deformation, linear and nonlinear modelling methods are discussed. Due to their high flexibility, large workspace, and high repeatability, industrial robots are widely used in roughing and semifinishing fields. However, their low machining accuracy and low stability limit further development of industrial robots in the machining field, with low stiffness being the most significant factor. The stiffness of industrial robots is affected by the joint deformation, transmission mechanism, friction, environment, and coupling of these factors. Moreover, the stiffness of a robot has a nonlinear distribution throughout the workspace, and external forces during processing cause irregular deviations of the robot, thereby affecting the machining accuracy and surface quality of the workpiece. Many scholars have researched identifying the stiffness of industrial robots and have proposed methods for improving the performance of industrial robots, mainly by optimizing the body structure of the robot and compensating for deformation errors with stiffness models. This paper reviews recent research on the stiffness modelling of industrial robots, which can be broadly classified as finite element analysis (FEA), matrix structure analysis (MSA), and virtual joint modelling (VJM) methods. Each method is studied from three aspects: algorithms, implementation, and limitations. In addition, common measurement techniques have been introduced for measuring deformation. Further research directions are also discussed. [ABSTRACT FROM AUTHOR]

Due to their high flexibility, large workspace, and high repeatability, industrial robots are widely used in roughing and semifinishing fields. However, their low machining accuracy and low stability limit further development of industrial robots in the machining field, with low stiffness being the most significant factor. The stiffness of industrial robots is affected by the joint deformation, transmission mechanism, friction, environment, and coupling of these factors. Moreover, the stiffness of a robot has a nonlinear distribution throughout the workspace, and external forces during processing cause irregular deviations of the robot, thereby affecting the machining accuracy and surface quality of the workpiece. Many scholars have researched identifying the stiffness of industrial robots and have proposed methods for improving the performance of industrial robots, mainly by optimizing the body structure of the robot and compensating for deformation errors with stiffness models. This paper reviews recent research on the stiffness modelling of industrial robots, which can be broadly classified as finite element analysis (FEA), matrix structure analysis (MSA), and virtual joint modelling (VJM) methods. Each method is studied from three aspects: algorithms, implementation, and limitations. In addition, common measurement techniques have been introduced for measuring deformation. Further research directions are also discussed.

A new index for a precise calculation of a manipulator’s stiffness isotropy is introduced. The proposed index is compared with the conventionally used stiffness isotropy index by making use of the investigation on R-CUBE manipulator. The proposed index is shown to produce relatively more precise results from which a higher number of isotropic poses are detected.

The paper addresses a problem of robotic manipulator calibration in real industrial environment. The main contributions are in the area of the elastostatic parameter identification. In contrast to other works the considered approach takes into account the elastic properties of both links and joints. Particular attention is paid to the practical identifiability of the model parameters, which completely differs from the theoretical one that relies on the rank of the observation matrix only, without taking into account essential differences in the model parameter magnitudes and the measurement noise impact. This problem is relatively new in robotics and essentially differs from that arising in geometrical calibration. To solve the problem, physical algebraic and statistical model reduction methods are proposed. They are based on the stiffness matrix sparseness taking into account the physical properties of the manipulator elements, structure of the observation matrix and also on the heuristic selection of the practically non-identifiable parameters that employ numerical analyses of the parameter estimates. The advantages of the developed approach are illustrated by an application example that deals with the elastostatic calibration of an industrial robot in a real industrial environment. [ABSTRACT FROM AUTHOR]

A new index for a precise calculation of a manipulator's stiffness isotropy is introduced. The proposed index is compared with the conventionally used stiffness isotropy index by making use of the investigation on R-CUBE manipulator. The proposed index is shown to produce relatively more precise results from which a higher number of isotropic poses are detected. [ABSTRACT FROM AUTHOR]