Kinematic analysis of overconstrained manipulators with partial subspaces using decomposition method

SUMMARY Overconstrained manipulators in lower subspaces with unique motions can be created and analyzed. However, far too little attention has been paid to creating a generic method for overconstrained manipulators kinematic analysis. This study aimed to evaluate a generic methodology for kinematic analysis of overconstrained parallel manipulators with partial subspaces (OPM-PS) using decomposition to parallel manipulators (PMs) in lower subspaces. The theoretical dimensions of the method are depicted, and the use of partial subspace for overconstrained manipulators is portrayed. The methodology for the decomposition method is described and exemplified by designing and evaluating the method to two overconstrained manipulators with 5 degrees of freedom (DoF) and 3 DoF. The inverse kinematic analysis is detailed with position analysis and Jacobian along with the inverse velocity analysis. The workspace analysis for the manipulators using the methodology is elaborated with numerical results. The results of the study show that OPM-PS can be decomposed into PMs with lower subspace numbers. As imaginary joints are being utilized in the proposed methodology, it will create additional data to consider in the design process of the manipulators. Thus, it becomes more beneficial in design scenarios that include workspace as an objective.

Kinematics of a planar slider-crank linkage in screw form

This paper investigates the forward and inverse kinematics in screw coordinates for a planar slider-crank linkage. According to the definition of a screw, both the angular velocity of a rigid body and the linear velocity of a point on it are expressed in screw components. Through numerical integration on the velocity solution, we get the displacement. Through numerical differential interpolation of velocity, we gain the acceleration of any joint. Traditionally, position and angular parameters are usually the only variables for establishing the displacement equations of a mechanism. For a series mechanism, the forward kinematics can be expressed explicitly in the variable of position parameters while the inverse kinematics will have to resort to numerical algorithms because of the multiplicity of solution. For a parallel mechanism, the inverse kinematics can be expressed explicitly in the variable of position parameters of the end effector while the forward kinematics will have to resort to numerical algorithms because of the nonlinearity of system. Therefore this will surely lead to second order numerical differential interpolation for the calculation of accelerations. The most prominent merit of this kinematic algorithm is that we only need the first order numerical differential interpolation for computing the acceleration. To calculate the displacement, we also only need the first order numerical integral of the velocity. This benefit stems from the screw the coordinates of which are velocity components. The example of planar four-bar and five-bar slider-crank linkages validate this algorithm. It is especially suited to developing numerical algorithms for forward and inverse velocity, displacement and acceleration of a linkage.

Failure Prediction of Open-pit Mine Landslide Containing Complex Geological Structure using Inverse Velocity Method: A Case Study in West Open-Pit mine, Pingzhuang, China

In the field of open-pit geological risk management, landslide failure time prediction is one of the important topics. Based on the analysis of displacement monitoring data, the inverse velocity method (IVM) has become an effective method to solve this issue. In order to improve the reliability of landslide prediction, four filters were used to test the velocity time series, and the effect of landslide failure time prediction was compared and analyzed. The IVM is used to predict the failure time of open-pit coal mine landslide. The results show that the sliding process of landslide can be divided into three stages based on the IVM: the initial attenuation stage (regressive stage), the second attenuation stage (progressive stage), the linear reduction stage (autoregressive stage). The accuracy of the IVM is closely related to the measured noise of the monitoring equipment and the natural noise of the environment, which will affect the identification of different deformation stages. Compared with the raw data and the exponential smoothing filter (ESF) models, the fitting effect of short-term smoothing filter (SSF) and long-term smoothing filter (LSF) in the linear autoregressive stage is better. A slope displacement pixel difference method based on fitting accuracy and field monitoring signals is proposed to determine the point onset-of-acceleration (OOA) that is very important role for landslide prediction. A stratified prediction method combining SSF and LSF is proposed. The prediction method is divided into two levels, and the application of this method is given.

Mathematical Modeling, Design Validation, and Simulation of Morphing Mechanism for Winglet Applications

Presented within this thesis is the preliminary design phases for the development of a morphing winglet mechanism. The mathematical models and analyses conducted within this thesis provide the means for bringing the design concept stage to the testing and validation phases. The kinematic modeling of a proposed design is developed. The inverse kinematics of the system are used to determine the required inputs to meet the range of motion. The velocity models for the system are established for both the forward and inverse cases. The inverse velocity models are used to establish a synchronous behaviour between the two serial linkages. Thus, allowing system operation as a redundantly actuated parallel mechanism. The results of implementation are evaluated for the initial and optimized designs. A proposed velocity profile is developed to facilitate control and desired operation of the system. This is then validated by the testing of the system response and error.

Mathematical Modeling, Design Validation, and Simulation of Morphing Mechanism for Winglet Applications

Presented within this thesis is the preliminary design phases for the development of a morphing winglet mechanism. The mathematical models and analyses conducted within this thesis provide the means for bringing the design concept stage to the testing and validation phases. The kinematic modeling of a proposed design is developed. The inverse kinematics of the system are used to determine the required inputs to meet the range of motion. The velocity models for the system are established for both the forward and inverse cases. The inverse velocity models are used to establish a synchronous behaviour between the two serial linkages. Thus, allowing system operation as a redundantly actuated parallel mechanism. The results of implementation are evaluated for the initial and optimized designs. A proposed velocity profile is developed to facilitate control and desired operation of the system. This is then validated by the testing of the system response and error.

Correlation between Acoustic Emission Behaviour and Dynamics Model during Three-Stage Deformation Process of Soil Landslide

Acoustic emission (AE) monitoring has become an optional technology to quantify slope deformation. However, there are still challenges in developing generic AE interpretation strategies. Dynamics and kinematics models are two physical methods for analysing slope stability, which appear to improve the interpretability of AE monitoring data. The aim of this study is to explore the change patterns and interrelations of dynamics, kinematics, and AE measurements using a model test and physical analysis, to further understand the development process of a progressive landslide. A model test is designed based on the kinematics model of landslide three-stage deformation. An equation between factor of safety (FoS) and thrust is proposed based on the mechanical model of a landslide test. There is a clear correspondence between the displacement and inverse velocity during the deformation-controlled process. Relationships are uncovered between the thrust and FoS as well as the thrust and acceleration. As a characteristic parameter of AE, ring down count (RDC) is able to quantify the deformation process of the soil slope. Moreover, acceleration and RDC can reflect the sudden change of the slope state and, hence, can be effective indicators for the early warning in a progressive landslide.

Integrated Analysis Method for Stability Analysis and Maintenance of Cut-Slope in Urban

In the process of constructing roads for the development of the city, cut-slopes are made by excavating mountains. However, these cut-slopes are degraded in strength by time-deterioration phenomenon, and progressive slope failure is caused. This study developed an integrated analysis method for stability analysis and maintenance of cut-slopes in urban. The slope stability analysis was performed using the finite element model, and the progressive slope failure by time-dependent deterioration was quantified by using the strength parameters of soil applying the strength reduction factor (SRF). The displacements until the slope failure by slope stability analysis were quantified by cumulative displacement curve, velocity curve, and inverse velocity curve and, applied to the slope maintenance method. The inverse-velocity curve applied to the prediction of the time of slope failure was regressed to the 1st linear equation in the brittle material and the 3rd polynomial equation in the ductile material. This is consistent with the proposed formula of Fukuzono and also shows similar behavior to the failure case in literature. In the future, integrated analysis method should be improved through additional research. And it should be applied to cut-slope to prevent disasters.

Movements, failure and climatic control of the Veslemannen rockslide, Western Norway

On September 5, 2019, the Veslemannen unstable rock slope (54,000 m3) in Romsdalen, Western Norway, failed catastrophically after 5 years of continuous monitoring. During this period, the rock slope weakened while the precursor movements increased progressively, in particular from 2017. Measured displacement prior to the failure was around 19 m in the upper parts of the instability and 4–5 m in the toe area. The pre-failure movements were usually associated with precipitation events, where peak velocities occurred 2–12 h after maximum precipitation. This indicates that the pore-water pressure in the sliding zones had a large influence on the slope stability. The sensitivity to rainfall increased greatly from spring to autumn suggesting a thermal control on the pore-water pressure. Transient modelling of temperatures suggests near permafrost conditions, and deep seasonal frost was certainly present. We propose that a frozen surface layer prevented water percolation to the sliding zone during spring snowmelt and early summer rainfalls. A transition from possible permafrost to a seasonal frost setting of the landslide body after 2000 was modelled, which may have affected the slope stability. Repeated rapid accelerations during late summers and autumns caused a total of 16 events of the red (high) hazard level and evacuation of the hazard zone. Threshold values for velocity were used in the risk management when increasing or decreasing hazard levels. The inverse velocity method was initially of little value. However, in the final phase before the failure, the inverse velocity method was useful for forecasting the time of failure. Risk communication was important for maintaining public trust in early-warning systems, and especially critical is the communication of the difference between issuing the red hazard level and predicting a landslide.