Theoretical and Experimental Study of the Dynamics of the Tripod-Ball Sliding Joint With Clearance

Clearance is inevitable in the kinematic joints of mechanisms. In this paper the dynamic behavior of a crank-slider mechanism with clearance in its tripod-ball sliding joint is investigated theoretically and experimentally. The mathematical model of this new-type joint is established, and the new concepts of basal system and active system are put forward. Based on the mode-change criterion established in this paper, the consistent equations of motion in full-scale are derived by using Kane method. The experimental rig was set up to measure the effects of the clearance on the dynamic response. Corresponding experimental studies verify the theoretical results satisfactorily. In addition, due to the nonlinear elements in the improved mathematical model of the joint with clearance, the chaotic responses are found in numerical simulation.

Effects of Initial Geometric Imperfections on Parametric Instability of Rectangular Plates

The authors present a rational analysis of the effect of initial geometric imperfections on the dynamic behaviour of rectangular plates activated by a parametric excitation. This subject has been extensively investigated theoretically in the past, but no experimental data seems to be complete enough to validate the theory. The main objective of this investigation is to fill this void by performing experimental tests on geometrically imperfect plates, and to highlight the geometric imperfection’s influence on resonance’s curves. The study is carried out for an isotropic, elastic, homogeneous, and thin rectangular plate. The plate under investigation is subjected to the action of an in-plane force uniformly distributed along two opposite edges, is initially stress free and simply supported. Theoretical calculation and experimental tests are performed. In the theoretical approach, a dynamic version of the Von Kármán non-linear theory is used to evaluate the lateral displacement of the plate. The test rig used in the experimentation simulates simply supported edges and can accept plates with different aspect ratio. The test plates are pre-formed with lateral deflection or geometrical imperfections, in a shape corresponding to various vibration modes. Comparison between experimental and theoretical results reveals good agreement and allows the determination of the theory’s limitations. The theory used correctly describes the behaviour of the plate when imperfection amplitude is inferior to the plate thickness.

Experimental Non-Linear Model Updating Applied in Cylindrical Journal Bearings

The present paper proposes the use of non linear model updating applying unrestricted optimization method, in order to obtain a methodology, which allows the calibration of mathematical models in rotating systems. An experimental set up for this purpose consists of a symmetric rotor, on a rigid foundation supported by two hidrodynamic cylindrical bearings and with a central disk of considerable mass, working as na unbalancing excitation force. Once the numeric and experimental values are obtained, error vectors are defined, which are the minimization parameters, through the variation of the numeric model parameters. The method presented satisfactory results, as it was able to calibrate the mathematical model, and then to obtain reliable responses for the physical system studied. The research also presents a contribution for the rotating machine desing area as it presents a relatively simple methodology on the updating and revalidation of computacional models for machines and structures.

Experimental Response of a Preloaded Vibro-Impacting Hertzian Contact

This paper concerns the non-linear dynamic response of a vibro-impacting Hertzian contact. Sinusoidal and random external normal forces are considered. We focus on the primary resonance and include vibro-impact responses in order to analyze the main characteristics of the system associated to both Hertzian and contact loss non-linearities. Under very small input amplitude, contact exhibits an almost linear resonance. Linearized resonance frequency and damping ratio are identified. Increasing the external input amplitude, the softening behaviour induced by Hertzian nonlinear stiffness is clearly demonstrated for both sinusoidal and random inputs. For higher input amplitude, system exhibits vibro-impacts. The contact loss non-linearity strongly governs the dynamic behaviour of the system.

An Experimental Approach to the Design of PVDF Modal Sensors

The principle of modal sensing is based on the use of a shaped PVDF piezoelectric film measuring strains on the surface of a bending beam and acting as a modal filter. So far, the use of this type of sensors has remained confined to studies involving uniform structures with classical boundary conditions. The goal of this paper is to present an experimental methodology for the design of a shaped modal sensor applicable to an non-uniform Euler-Bernoulli beam with arbitrary boundary conditions. This approach is illustrated with test data collected on a cantilever beam structure with a laser Doppler velocimeter.

The Robust Adaptive Control of Free-Floating Space Manipulator Systems

In this paper, the kinematics and dynamics of free-floating space manipulator systems are analyzed, and it is shown that the Jacobian matrix and the dynamic equations of the system are nonlinearly dependent on inertial parameters. In order to overcome the above problems, the system is modeled as under-actuated robot system, and the idea of augmentation approach is adopted. It is demonstrate that the augmented generalized Jacobian matrix and the dynamic equations of the system can be linearly dependent on a group of inertial parameters. Based on the results, the robust adaptive control scheme for free-floating space manipulator with uncertain inertial parameters to track the desired trajectory in workspace is proposed, and a two-link planar space manipulator system is simulated to verify the proposed control scheme. The proposed control scheme is computationally simple, because we choose to make the controller robust to the uncertain inertial parameters rather than explicitly estimating them online. In particular, it require neither measuring the position, velocity and acceleration of the floating base with respect to the orbit nor controlling the position and attitude angle of the floating base.

Sensorless Modal Stabilization for Three-Link Robotic Arm With Elastic Wrist Drive Belt

A control system for a three-link direct-drive robotic manipulator with inherent structural flexibilities is presented. The structural flexibilities introduce undesirable vibration modes which may affect operation of the robot motion controller, resulting in destabilization of the closed-loop system. This represents a major limiting factor for implementation of a conventional controller designed solely for the rigid body dynamics of the robotic manipulator. The fundamental idea in the presented approach is to use a composite controller which consists of a trajectory-tracking section designed for the rigid-body dynamics and a vibration-damping compensator added for attenuation of the dominant flexible dynamics. The vibration damping compensator operates on estimated states of the dominant flexible dynamics obtained from a reduced-order state observer. A mechanism is implemented which allows the robotic manipulator to move through or hold in positions where the dominant flexible dynamics is unobservable and uncontrollable. Results of laboratory tests document that the presented approach leads to improved stability and control performance.

Analysis of Varying Natural Frequencies and Damping Ratios of a Sample Parallel Manipulator Throughout its Workspace Using Linearized Equations of Motion

This article investigates the dynamic properties of robotic manipulators of parallel architecture. In particular, the dependency of the dynamic equations on the manipulator’s configuration within the workspace is analyzed. The proposed approach is to linearize the dynamic equations locally throughout the workspace and to plot the corresponding natural frequencies and damping ratios. While the results are only applicable for small velocities of the manipulator, they present a first step towards the classification of the nonlinear dynamics of parallel manipulators. The method is applied to a sample manipulator with two degrees-of-freedom. The corresponding numerical results demonstrate the extreme variation of its natural frequencies and damping ratios throughout the workspace.

Moving Force Identification for Multi-Span Bridges by Using Acceleration Measurements

This paper reports some initial findings in the attempt to develop a robust method to identify more than one moving force on multi-span non-uniform continuous bridges. To keep the number of unknowns in the moving force identification problem to a minimum, the modified beam vibration functions are chosen as the assumed modes of a multi-span bridge. These modified beam vibration functions satisfy the zero deflection conditions at all the intermediate supports as well as the boundary conditions at the two ends of the bridge. The least squares method is used to solve the inverse problem to get the closest approximation to the moving forces. The pseudo-inverse to obtain the solution to the inverse problem is obtained by singular value decomposition. Only acceleration measurements are used for the moving force identification. The results show that this method is applicable and robust.

Input-Shaped Control of Gantry Cranes: Simulation and Curriculum Development

Knowledge of vibrations and controls has increased significantly by utilizing emerging computer capabilities. Engineering education should embrace this technology through computer simulations that predict and display the dynamic response of interesting systems. For example, manipulating payloads with an overhead gantry crane can be challenging due to the oscillations induced by the crane motion. The problem gets increasingly difficult when the work environment is cluttered with obstacles. This paper describes a simple input shaping solution to the vibration problem and shows how this problem and concept were integrated into the curriculum of an undergraduate system dynamics and controls course at the Georgia Institute of Technology. Furthermore, an educational tool is used to gather data on how crane operators attempt to navigate around obstacles. The results show that input shaping reduces the likelihood of collisions between the payload and obstacles, while at the same time allowing operators to be more aggressive in selecting navigation paths.