On the elastodynamics of a five-axis lightweight anthropomorphic robotic arm

This paper presents elastodynamic modeling and analysis for a five-axis lightweight robotic arm. Natural frequencies are derived and visualized within the dexterous workspace to show the overall performances and compare them to the frequencies when the robotics is with payload. The comparison shows that the payload has a relatively small influence to the first- and second-order frequencies. Sensitivity analysis is conducted, and the system's frequency is more sensitive to the second joint stiffness than the others. Moreover, observations from the displacement response analysis reveal that the robotics produces linear elastic displacements of the same level between the loaded and unloaded working modes but larger rotational deflections under the loaded working condition. The main contribution of this work lies in that a systematic approach of elastodynamic analysis for serial robotic manipulators is formulated, where the arm gravity and external load are taken into account to investigate the dynamic behaviors of the robotic arms, i.e., frequencies, sensitivity analysis, and displacement responses, under the loaded mode.

A Screw Theory-Based Semi-Analytical Approach for Elastodynamics of the Tricept Robot

Taking the well-known Tricept robot as an example, this paper presents a semi-analytical approach for elastodynamic modeling of five or six degrees of freedom (DOF) hybrid robots composed of a 3-DOF parallel mechanism plus a 2- or 3-DOF wrist. Drawing heavily on screw theory combined with structural dynamics, the kinetic and elastic potential energies of the parallel mechanism and of the wrist are formulated using the dual properties of twist/wrench systems and a static condensation technique. This results in a 9-DOF dynamic model that enables the lower-order dynamic behavior over the entire workspace to be estimated in a very efficient and accurate manner. The lower-order natural frequencies and mode shapes estimated by the proposed approach are shown to have very good agreement with those obtained by a full-order finite element (FE) model. It thus provides a very time-effective tool for optimal design within a virtual prototyping framework for hybrid robot-based machine tools.

Elastodynamic Modeling and Analysis for an Exechon Parallel Kinematic Machine

As a newly invented parallel kinematic machine (PKM), Exechon has attracted intensive attention from both academic and industrial fields due to its conceptual high performance. Nevertheless, the dynamic behaviors of Exechon PKM have not been thoroughly investigated because of its structural and kinematic complexities. To identify the dynamic characteristics of Exechon PKM, an elastodynamic model is proposed with the substructure synthesis technique in this paper. The Exechon PKM is divided into a moving platform subsystem, a fixed base subsystem and three limb subsystems according to its structural features. Differential equations of motion for the limb subsystem are derived through finite element (FE) formulations by modeling the complex limb structure as a spatial beam with corresponding geometric cross sections. Meanwhile, revolute, universal, and spherical joints are simplified into virtual lumped springs associated with equivalent stiffnesses and mass at their geometric centers. Differential equations of motion for the moving platform are derived with Newton's second law after treating the platform as a rigid body due to its comparatively high rigidity. After introducing the deformation compatibility conditions between the platform and the limbs, governing differential equations of motion for Exechon PKM are derived. The solution to characteristic equations leads to natural frequencies and corresponding modal shapes of the PKM at any typical configuration. In order to predict the dynamic behaviors in a quick manner, an algorithm is proposed to numerically compute the distributions of natural frequencies throughout the workspace. Simulation results reveal that the lower natural frequencies are strongly position-dependent and distributed axial-symmetrically due to the structure symmetry of the limbs. At the last stage, a parametric analysis is carried out to identify the effects of structural, dimensional, and stiffness parameters on the system's dynamic characteristics with the purpose of providing useful information for optimal design and performance improvement of the Exechon PKM. The elastodynamic modeling methodology and dynamic analysis procedure can be well extended to other overconstrained PKMs with minor modifications.

Elastodynamic Modeling and Simulation of an Axially Accelerating Beam

This paper aims to develop an accurate nonlinear mathematical model which may describe the coupled in-plane motion of an axially accelerating beam. The Extended Hamilton’s Principle was utilized to derive the partial differential equations governing the motion of a simply supported beam. The set of the ordinary differential equations were obtained by means of the assumed mode method. The derived elastodynamic model took into account the geometric non-linearity, the time-dependent axial velocity and the coupling between the transverse and longitudinal vibrations. The developed equations were solved numerically using the Runge-Kutta method and the obtained results were presented in terms of the vibrational response graphs and the system natural frequencies. The system dynamic characteristics were explored with a major focus on the influence of the velocity, acceleration and the excitation force frequency. The obtained results showed that the natural frequency decreased significantly at high axial velocities. Also it was found that the system may exhibit unstable behavior at high accelerations.

Kinetoelastodynamics Modeling and Analysis of Spatial Parallel Mechanism

The nonlinear elastodynamic modeling and analysis of the 4-UPS-UPU spatial 5-degree-of-freedom parallel mechanism are investigated. The kinetoelastodynamics theory is used to derive the elastic dynamic equations of 4-UPS-UPU spatial parallel mechanism. In order to grasp the effect of geometric nonlinearity on dynamic behaviors, such as displacement error output, velocity error output, acceleration error output, stress of driving limbs, and natural frequencies, the variations of dynamic behaviors considering geometric nonlinearity and without considering geometric nonlinearity are discussed, respectively. The numerical simulation results show the nonlinear elastodynamic model established can reasonably reflect the dynamic behaviors of 4-UPS-UPU spatial parallel mechanism with flexible driving limbs. And geometric nonlinearity is demonstrated to have significant impact on dynamic response and dynamic characteristics of spatial parallel mechanism. The researches can provide important theoretical base for the optimal design of spatial parallel mechanism.