Anisotropic force ellipsoid based multi-axis motion optimization of machine tools

The existing research of the motion optimization of multi-axis machine tools is mainly based on geometric and kinematic constraints, which aim at obtaining minimum-time trajectories and finding obstacle-free paths. In motion optimization, the stiffness characteristics of the whole machining system, including machine tool and cutter, are not considered. The paper presents a new method to establish a general stiffness model of multi-axis machining system. An analytical stiffness model is established by Jacobi and point transformation matrix method. Based on the stiffness model, feed-direction stiffness index is calculated by the intersection of force ellipsoid and the cutting feed direction at the cutter tip. The stiffness index can help analyze the stiffness performance of the whole machining system in the available workspace. Based on the analysis of the stiffness performance, multi-axis motion optimization along tool paths is accomplished by mixed programming using Matlab and Visual C++. The effectiveness of the motion optimization method is verified by the experimental research about the machining performance of a 7-axis 5-linkage machine tool. The proposed research showed that machining stability and production efficiency can be improved by multi-axis motion optimization based on the anisotropic force ellipsoid of the whole machining system.     

Basic Characteristics of a New Flexible Pneumatic Bending Joint

Several typical flexible pneumatic actuators （FPA） and different mechanical models describing their behaviors have been proposed, however, it is difficult to balance compliance and load capacity in conventional designs, and these models still have limitations in predicting behavior of FPAs. A new flexible pneumatic bending joint （FPBJ） with special anisotropic rigidity structure is proposed. The FPBJ is developed as an improvement with regard to existing types of FPA, and its principal characteristic is derived from the special anisotropic rigidity structure. With this structure, the load capacity in the direction perpendicular to bending plane is strengthened. The structure of the new FPBJ is explained and a mathematical model is derived based on Euler-Bernoulli beam model and Hook’s law. To obtain optimum design and usage, some key structure parameters and input-output characteristics are simulated. The simulation results reveal that the relationship between the structure parameters and FPBJ’s bending angle is nonlinear. At last, according to the simulation results, the FPBJ is manufactured with optional parameters and tested. The experimental results show that the joint’s statics characteristics are reflected by the mathematical model accurately when the FPBJ is deflated. The maximum relative error between simulation and experimental results is less than 6%. However, the model still has limitations. When the joint is inflated, the maximum relative error reaches 20%. This paper proposes a new flexible pneumatic bending joint which has sufficient load capacity and compliance, and the mathematical model provides theoretical guidance for the FPBJ’s structure design.     

Kinematics and dynamics analysis of a quadruped walking robot with parallel leg mechanism

It is desired to require a walking robot for the elderly and the disabled to have large capacity,high stiffness,stability,etc.However,the existing walking robots cannot achieve these requirements because of the weight-payload ratio and simple function.Therefore,Improvement of enhancing capacity and functions of the walking robot is an important research issue.According to walking requirements and combining modularization and reconfigurable ideas,a quadruped/biped reconfigurable walking robot with parallel leg mechanism is proposed.The proposed robot can be used for both a biped and a quadruped walking robot.The kinematics and performance analysis of a 3-UPU parallel mechanism which is the basic leg mechanism of a quadruped walking robot are conducted and the structural parameters are optimized.The results show that performance of the walking robot is optimal when the circumradius R,r of the upper and lower platform of leg mechanism are 161.7 mm,57.7 mm,respectively.Based on the optimal results,the kinematics and dynamics of the quadruped walking robot in the static walking mode are derived with the application of parallel mechanism and influence coefficient theory,and the optimal coordination distribution of the dynamic load for the quadruped walking robot with over-determinate inputs is analyzed,which solves dynamic load coupling caused by the branches’ constraint of the robot in the walk process.Besides laying a theoretical foundation for development of the prototype,the kinematics and dynamics studies on the quadruped walking robot also boost the theoretical research of the quadruped walking and the practical applications of parallel mechanism.     

Biped walking robot based on a 2-UPU+2-UU parallel mechanism

Existing biped robots mainly fall into two categories： robots with left and right feet and robots with upper and lower feet. The load carrying capability of a biped robot is quite limited since the two feet of a walking robot supports the robot alternatively during walking. To improve the load carrying capability, a novel biped walking robot is proposed based on a 2-UPU＋2-UU parallel mechanism. The biped walking robot is composed of two identical platforms（feet） and four limbs, including two UPU（universal-prismatic-universal serial chain） limbs and two UU limbs. To enhance its terrain adaptability like articulated vehicles, the two feet of the biped walking robot are designed as two vehicles in detail. The conditions that the geometric parameters of the feet must satisfy are discussed. The degrees-of-freedom of the mechanism is analyzed by using screw theory. Gait analysis, kinematic analysis and stability analysis of the mechanism are carried out to verify the structural design parameters. The simulation results validate the feasibility of walking on rugged terrain. Experiments with a physical prototype show that the novel biped walking robot can walk stably on smooth terrain. Due to its unique feet design and high stiffness, the biped walking robot may adapt to rugged terrain and is suitable for load-carrying.     

Mechanics unloading analysis and experimentation of a new type of parallel biomimetic shoulder complex

The structure design for high ratio of carrying capacity to deadweight is one of the challenges for the bionic mechanism, while the problem concerning high carrying capacity has not yet be solved for the existing shoulder complex. A new type biomimetic shoulder complex, which adopts 3-PSS/S(P for prismatic pair, S for spherical pair) spherical parallel mechanism (SPM), is proposed. The static equilibrium equations of each component are established by using the vector method and the equations for constrain forces with certain load are solved. Then the constrain force on the middle limb and that on the side limbs are compared in order to verify the unloading performance of the mechanism. In addition, the prototype mechanism of the shoulder complex is developed, and the force feedback experiment is conducted to verify the static analysis, which indicates that the middle limb suffers most of the external force and the effect of mechanics unloading is achieved. The 3-PSS/S spherical parallel mechanism is presented for the shoulder complex, and the realization of mechanics unloading is benefit for the improvement of the carrying capacity of the shoulder complex.     

Motion error compensation of multi-legged walking robots

Existing errors in the structure and kinematic parameters of multi-legged walking robots,the motion trajectory of robot will diverge from the ideal sports requirements in movement.Since the existing error compensation is usually used for control compensation of manipulator arm,the error compensation of multi-legged robots has seldom been explored.In order to reduce the kinematic error of robots,a motion error compensation method based on the feedforward for multi-legged mobile robots is proposed to improve motion precision of a mobile robot.The locus error of a robot body is measured,when robot moves along a given track.Error of driven joint variables is obtained by error calculation model in terms of the locus error of robot body.Error value is used to compensate driven joint variables and modify control model of robot,which can drive the robots following control model modified.The model of the relation between robot’s locus errors and kinematic variables errors is set up to achieve the kinematic error compensation.On the basis of the inverse kinematics of a multi-legged walking robot,the relation between error of the motion trajectory and driven joint variables of robots is discussed.Moreover,the equation set is obtained,which expresses relation among error of driven joint variables,structure parameters and error of robot’s locus.Take MiniQuad as an example,when the robot MiniQuad moves following beeline tread,motion error compensation is studied.The actual locus errors of the robot body are measured before and after compensation in the test.According to the test,variations of the actual coordinate value of the robot centroid in x-direction and z-direction are reduced more than one time.The kinematic errors of robot body are reduced effectively by the use of the motion error compensation method based on the feedforward.     

Typical gait analysis of a six-legged robot in the context of metamorphic mechanism theory

The equivalent mechanism of the system is often considered as one specific mechanism in most existing studies of multi-legged robots, however the equivalent mechanism is varying while the robot moves on the ground. Four typical tripod period gaits of a radial symmetrical six-legged robot are analyzed. Similar to the metamorphic mechanism, the locomotion of multi-legged robot is considered as a series of varying hybrid serial-parallel mechanisms by assuming the constraints of the feet on the ground with hinges. One gait cycle is divided into several periods, and in different walking period there is a specific equivalent mechanism corresponding to it, and the walking process of multi-legged robot is composed by these series of equivalent mechanisms. Walking performance can be got by analyzing these series of equivalent mechanisms. Kinematics model of the equivalent mechanism is established, workspaces of equivalent mechanisms are illustrated by simulation and a concept of static stability workspace is proposed to evaluate the static stability of these four gaits. A new method to calculate the stride length of multi-legged robots is presented by analyzing the relationship between the workspace of two adjacent equivalent parallel mechanisms in one gait cycle. The stride lengths of four gaits are given by simulations. Comparison of stride length and static stability among these four typical tripod gaits are given. It has been proved that mixed gait and insect-wave gait II have better static stability than mammal kick-off gait and insect-wave gait I. Insect-wave gait II displays its advantage on stride length while the height of robot body lower than 87 mm, mammal kick-off gait has superiority on stride length while the height of robot body higher than 115 mm, and insect-wave gait I shows its shortcoming in stride length. The proposed method based on metamorphic theory and combining the footholds and body height of robot provides a new method to comprehensive analyze the performance of multi-legged robot.     

Dynamics and Wheel’s Slip Ratio of a Wheel-legged Robot in Wheeled Motion Considering the Change of Height

The existing research on dynamics and slip ratio of wheeled mobile robot (WMR) are derived without considering the effect of height, and the existing models can not be used to analyze the dynamics performance of the robot with variable height while moving such as NOROS-Ⅱ. The existing method of dynamics modeling is improved by adding the constraint equation between perpendicular displacement of body and horizontal displacement of wheel into the constraint conditions. The dynamic model of NOROS-Ⅱ in wheel motion is built by the Lagrange method under nonholonomic constraints. The inverse dynamics is calculated in three different paths based on this model, and the results demonstrate that torques of hip pitching joints are inversely proportional to the height of robot. The relative error of calculated torques is less than 2% compared with that of ADAMS simulation, by which the validity of dynamic model is verified. Moreover, the relative horizontal motion between fore?hind wheels and body is produced when the height is changed, and thus the accurate slip ratio can not be obtained by the traditional equation. The improved slip ratio equations with the parameter of the vertical velocity of body are introduced for fore wheels and hind wheels respectively. Numerical simulations of slip ratios are conducted to reveal the effect of varied height on slip ratios of different wheels. The result shows that the slip ratios of fore?hind wheels become larger?smaller respectively as the height increases, and as the height is reduced, the reverse applies. The proposed research of dynamic model and slip ratio based on the robot height provides the effective method to analyze the dynamics of WMRs with varying height.     

Synthetical efficiency-based optimization for the power distribution of power-split hybrid electric vehicles

Now the optimization strategies for power distribution are researched widely, and most of them are aiming to the optimal fuel economy and the driving cycle must be preknown. Thus if the actual driving condition deviates from the scheduled driving cycle, the effect of optimal results will be declined greatly. Therefore, the instantaneous optimization strategy carried out on-line is studied in this paper. The power split path and the transmission efficiency are analyzed based on a special power-split scheme and the efficiency models of the power transmitting components are established. The synthetical efficiency optimization model is established for enhancing the transmission efficiency and the fuel economy. The identification of the synthetical efficiency as the optimization objective and the constrain group are discussed emphatically. The optimization is calculated by the adaptive simulated annealing （ASA） algorithm and realized on-line by the radial basis function （RBF）-based similar models. The optimization for power distribution of the hybrid vehicle in an actual driving condition is carried out and the road test results are presented. The test results indicate that the synthetical efficiency optimization method can enhance the transmission efficiency and the fuel economy of the power-split hybrid electric vehicle （HEV） observably. Compared to the rules-based strategy the optimization strategy is optimal and achieves the approximate global optimization solution for the power distribution. The synthetical efficiency optimization solved by ASA algorithm can give attentions to both optimization quality and calculation efficiency, thus it has good application foreground for the power distribution of power-split HEV.     

Topology Optimization of Compliant Mechanisms with Geometrical Nonlinearities Using the Ground Structure Approach

The majority of topology optimization of compliant mechanisms uses linear finite element models to find the structure responses.Because the displacements of compliant mechanisms are intrinsically large,the topological design can not provide quantitatively accurate result.Thus,topological design of these mechanisms considering geometrical nonlinearities is essential.A new methodology for geometrical nonlinear topology optimization of compliant mechanisms under displacement loading is presented.Frame elements are chosen to represent the design domain because they are capable of capturing the bending modes.Geometrically nonlinear structural response is obtained by using the co-rotational total Lagrange finite element formulation,and the equilibrium is solved by using the incremental scheme combined with Newton-Raphson iteration.The multi-objective function is developed by the minimum strain energy and maximum geometric advantage to design the mechanism which meets both stiffness and flexibility requirements, respectively.The adjoint method and the direct differentiation method are applied to obtain the sensitivities of the objective functions. The method of moving asymptotes(MMA) is employed as optimizer.The numerical example is simulated to show that the optimal mechanism based on geometrically nonlinear formulation not only has more flexibility and stiffness than that based on linear formulation,but also has better stress distribution than the one.It is necessary to design compliant mechanisms using geometrically nonlinear topology optimization.Compared with linear formulation,the formulation for geometrically nonlinear topology optimization of compliant mechanisms can give the compliant mechanism that has better mechanical performance.A new method is provided for topological design of large displacement compliant mechanisms.     

Adaptive walking of a quadrupedal robot based on layered biological reflexes

A multiple-legged robot is traditionally controlled by using its dynamic model.But the dynamic-model-based approach fails to acquire satisfactory performances when the robot faces rough terrains and unknown environments.Referring animals’ neural control mechanisms,a control model is built for a quadruped robot walking adaptively.The basic rhythmic motion of the robot is controlled by a well-designed rhythmic motion controller(RMC) comprising a central pattern generator(CPG) for hip joints and a rhythmic coupler(RC) for knee joints.CPG and RC have relationships of motion-mapping and rhythmic couple.Multiple sensory-motor models,abstracted from the neural reflexes of a cat,are employed.These reflex models are organized and thus interact with the CPG in three layers,to meet different requirements of complexity and response time to the tasks.On the basis of the RMC and layered biological reflexes,a quadruped robot is constructed,which can clear obstacles and walk uphill and downhill autonomously,and make a turn voluntarily in uncertain environments,interacting with the environment in a way similar to that of an animal.The paper provides a biologically inspired architecture,with which a robot can walk adaptively in uncertain environments in a simple and effective way,and achieve better performances.     

Numerical simulation and experimental research on passive hydrodynamic bearing in a blood pump

The current research of hydrodynamic bearing in blood pump mainly focuses on the bearing structure design.Compared with the typical plane slider bearing and Rayleigh step bearing,spiral groove bearing has excellent performance in load-carrying capacity.However,the load-carrying capacity would decrease significantly with increasing flow rate in conventional designs.In this paper,the special treatment is made to the upper spiral groove bearing to make sure that both the circulatory flowing and load-carrying capacity are high.Three-dimensional computational fluid dynamics(CFD) models in the space between rotor and shaft are developed by using FLUENT software.Effects of groove number,film height and groove depth on load-carrying capacity of the spiral groove bearings are investigated by orthogonal experiment design.The experimental results show that film height is the most remarkable factor to the load-carrying capacity.The variation tendency of load-carrying capacity reveals that the best combination of geometry is the one with groove number of 8,film height 0.03 mm and groove depth 0.08 mm.The velocity and pressure distributions in spiral groove bearings are also analyzed,and the analysis result shows that the distributions are in conformity with the design of the blood pump based on the principle of hydrodynamic bearing.The displacement of the rotor with the best combination parameters is tested by using laser displacement sensors,the testing result shows that the suspending performance is satisfactory both in axial and radial directions.This research proposes a bearing design method which has sufficient load-carrying capacity to support rotor as an effective passive hydrodynamic bearing.     

LOADING CAPACITY ANALYSIS OF THE MISALIGNED CONICAL-CYLINDRICAL BEARING WITH NON NEWTONIAN LUBRICANTS

A novel numerical method to lubricate a conventional finite diameter conical-cylindrical bearing with a non-Newtonian lubricant, while adhering to the power-law model, is presented. The elastic deformation of bearing and varied viscosity of lubrication due to the pressure distribution of film thickness are also considered. Simulation results indicate that the normal load carrying capacity is more pronounced for higher values of flow behavior index n, higher eccentricity ratios and larger misalignment factors. It is found that the viscosity-pressure to the effect of lubricant viscosity is significant.     

SELF-ALIGNING EVEN LOAD MECHANISM OF MULTI-ROW BEARINGS OF LARGE STRIP ROLLING MILL

The load distribution of multi-row bearings of large strip rolling mill is fully analyzed by 3D contact boundary element method (BEM). It is found out that bearings are frequently worn out due to serious uneven load on the multi-row rollers. The constraint mechanism of the previous rolling system is found to be unreasonable by theoretical analysis on heavy machinery structure. A mechanism of self-aligning even load for workroll bearing of 2 050 mm hot rolling mill of Baoshan I&S Co. is developed. This device is manufactured with particular regard to the structure of 2 050 mm hot rolling mill mentioned above. Hence, uneven load on multi-row bearings is greatly relieved and their lives are remarkably prolonged. Meanwhile, theoretical analysis and on-spot tests prove the rationality and validity of the device.     

Multi-objective Topology Optimization of Thermo-mechanical Compliant Mechanisms

The material characteristics of a structure will change with temperature variation,and will induce stress within the structure.Currently,the optimal design for the topology of compliant mechanisms is mainly performed in single physical field.However,when compliant mechanisms work in high temperature environments,their displacement outputs are generated not only by mechanical load,but also by the temperature variation which may become the prominent factor.Therefore,the influence of temperature must be considered in the design.In this paper,a novel optimization method for multi-objective topology of thermo-mechanical compliant mechanisms is presented.First,the thermal field is analyzed with finite-element method,where the thermal strain is taken into account in the constitutive relation,and the equivalent nodal thermal load is derived with the principle of virtual work.Then the thermal load is converted into physical loads in elastic field,and the control equation of the thermo-mechanical compliant mechanism is obtained.Second,the mathematical model of the multi-objective topology optimization is built by incorporating both the flexibility and stiffness.Meanwhile,the coupling sensitivity function and the sensitivity analysis equations of thermal steady-state response are derived.Finally,optimality criteria algorithm is employed to obtain numerical solution of the multi-objective topology optimization.Numerical examples show that the compliant mechanisms have better performance and are more applicable if the temperature effect is taken into account in the design process.The presented modeling and analysis methods provide a new idea and an effective approach to topology optimization of compliant mechanisms in electrothermic coupling field and multiphysics fields.     

APPROACH TO IMPROVEMENT OF ROBOT TRAJECTORY ACCURACY BY DYNAMIC COMPENSATION

Some dynamic factors, such as inertial forces and friction, may affect the robot trajectory accuracy. But these effects are not taken into account in robot motion control schemes. Dynamic control methods, on the other hand, require the dynamic model of robot and the implementation of new type controller. A method to improve robot trajectory accuracy by dynamic compensation in robot motion control system is proposed. The dynamic compensation is applied as an additional velocity feedforward and a multilayer neural network is employed to realize the robot inverse dynamics. The complicated dynamic parameter identification problem becomes a learning process of neural network connecting weights under supervision. The finite Fourier series is used to activate each actuator of robot joints for obtaining training samples. Robot control system, consisting of an industrial computer and a digital motion controller, is implemented. The system is of open architecture with velocity feedforward function. The proposed m     

Rapid optimization of tension distribution for cable-driven parallel manipulators with redundant cables

The solution of tension distributions is infinite for cable-driven parallel manipulators(CDPMs) with redundant cables. A rapid optimization method for determining the optimal tension distribution is presented. The new optimization method is primarily based on the geometry properties of a polyhedron and convex analysis. The computational efficiency of the optimization method is improved by the designed projection algorithm, and a fast algorithm is proposed to determine which two of the lines are intersected at the optimal point. Moreover, a method for avoiding the operating point on the lower tension limit is developed. Simulation experiments are implemented on a six degree-of-freedom(6-DOF) CDPM with eight cables, and the results indicate that the new method is one order of magnitude faster than the standard simplex method.The optimal distribution of tension distribution is thus rapidly established on real-time by the proposed method.     

Design and dynamic modeling of a 2-DOF decoupled flexure-based mechanism

Flexure mechanisms with decoupled characteristics have been widely utilized in precision positioning applications.However,these mechanisms suffer from either slow response or low load capability.Furthermore,asymmetric design always leads to thermal error.In order to solve these issues,a novel 2-DOF decoupled mechanism is developed by monolithically manufacturing sets of statically indeterminate symmetric(SIS) flexure structures in parallel.Symmetric design helps to eliminate the thermal error and Finite Element Analysis(FEA) results show that the maximum coupling ratio between X and Y axes is below 0.25% when a maximum pretension force of 200 N is applied.By ignoring the mass effect,all the SIS flexure structures are simplified to "spring-damper" components,from which the static and dynamics model are derived.The relation between the first resonant frequency of the mechanism and the load is investigated by incorporating the load mass into the proposed dynamics model.Analytical results show that even with a load of 0.5 kg,the first resonant frequency is still higher than 300 Hz,indicating a high load capability.The mechanism’s static and dynamic performances are experimentally examined.The linear stiffnesses of the mechanism at the working platform and at the driving point are measured to be 3.563 0 N·μm-1 and 3.362 1 N·μm-1,respectively.The corresponding estimation values from analytical models are 3.405 7 N·μm-1 and 3.381 7 N·μm-1,which correspond to estimation errors of-4.41% and 0.6%,respectively.With an additional load of 0.16 kg,the measured and estimated first resonant frequencies are 362 Hz and 365 Hz,respectively.The estimation error is only 0.55%.The analytical and experimental results show that the developed mechanism has good performances in both decoupling ability and load capability;its static and dynamic performance can be precisely estimated from corresponding analytical models.The proposed mechanism has wide potentials in precision positioning applications.     

ANALYSIS OF TIPOVER STABILITY FOR NOVEL SHAPE SHIFTING MODULAR ROBOT

A novel three-module robot has been introduced. It can change its configuration to adapt to the uneven terrain and to improve its tipover stability. This three-module tracked robot has three kinds of symmetry configuration. They are line type, triangle type, and row type. After the factors and the countermeasures of mobile robot's tipover problem are analyzed, stability pyramid and tipover stability index are proposed to globally determinate the mobile robot's static stability and dynamic stability. The shape shifting robot is tested by this technique under the combined disturbance of pitch, roll and yaw in simulation. The simulation result shows that this technique is effective for the analysis of mobile robot's tipover stability, especially for the reconfigurable or shape shifting modular robot. Experiments on three symmetry configurations are made under unstructured environments. The environment experiment shows the same result as that of the simulation that the triangle type configuration has the best stability. Both simulation and experiment provide a valid reference for the reconfigurable robot's potential application.