Zhongqin Lin

Determination of the Identifiable Parameters in Robot Calibration Based on the POE Formula

This paper presents an analytical approach to determine and eliminate the redundant model parameters in serial-robot kinematic calibration based on the product of exponentials formula. According to the transformation principle of the Lie algebra se(3) between different frames, the connection between the joints twist errors and the links geometric ones is established. Identifiability analysis shows that the redundant errors are simply equivalent to the commutative elements of the robots joint twists. Using the Lie bracket operation of se(3), a linear partitioning operator can be constructed to analytically separate the identifiable parameters from the system error vector. Then, error models satisfying the completeness, minimality, and model continuity requirements can be obtained for any serial robot with all combinations and configurations of revolute and prismatic joints. The conventional conclusion that the maximum number of independent parameters is 4r + 2p + 6 in a generic serial robot with r revolute and p prismatic joints is verified. Using the quotient manifold of the Lie group SE(3), the links geometric errors and the joints offset errors can be integrated as a whole, such that all these errors can be identified simultaneously. To verify the effectiveness of the proposed method, calibration simulations and experiments are conducted on an industrial six-degree-of-freedom (DoF) serial robot.

Modular Calculation of the Jacobian Matrix and Its Application to the Performance Analyses of a Forging Robot

This paper presents a modular approach for the calculation of the Jacobian matrix based on the composite modeling method. By decomposing the complicated mechanisms into simpler modules, the system Jacobian matrices can be obtained from the separated modules local ones, which can be derived much easier. Additionally, the kinematics and dynamics models of newly designed mechanisms can be constructed fast by reusing the predefined modules, as well as the system Jacobian matrices. Therefore, the Jacobian matrix based performance indices can be obtained with this modular approach easily to characterize kinematic and dynamic manipulability, and the force capability. In order to verify the proposed method, a forging robot, which can be simplified as a complex planar 2-d.o.f. mechanism with a multiple closed-loop structure, is studied as an example. The manipulability ellipse, dynamic manipulability ellipse and inertia matching ellipse are analyzed using this approach, and the performance measures with respect to the joint space are illustrated to describe the kinematic and dynamic capability of the manipulator intuitively. The research work in this paper can serve as the basis for designing and optimizing forging robots, and motion planning for the forging process.

The Principal Axes Decomposition of Spatial Stiffness Matrices

This paper presents an alternative decomposition of spatial stiffness matrices based on the concept of compliant axes. According to the congruence transformation of spatial stiffness, the coordinate-invariant aspects, which are referred to as the central principal components of the 6 × 6 symmetric positive semidefinite matrices, can be derived uniquely. The proposed decomposition is free from the eigenvalue problems of the 6 × 6 stiffness matrices so that both Plückers ray and axis coordinates can be utilized to characterize the elastic systems force-deflection behavior. Hence, an arbitrary spatial stiffness matrix can be uniquely decomposed into two sets of orthogonal spring wrenches with finite and infinite pitches, respectively. The decomposed wrenches with finite pitches correspond to the stiffness wrench-compliant axes, along which linear deformations produce only wrenches parallel to them. As a result, three torsional and three screw springs are required, at the most, to realize a given spatial stiffness. Using the principal axes decomposition, some physical appreciations, such as the center of stiffness, the wrench-compliant axes, and the correspondence of compliance and stiffness, can be derived to reveal the inherent structure of spatial stiffness in an intuitive manner. In order to verify the effectiveness of the proposed method, two numerical examples are intensively studied with comparison to the eigenscrew decomposition. In addition, a potential application of the proposed stiffness decomposition method is also provided for the structural compliance modeling of flexible links in robot manipulators.

Stabilized multi-domain simulation algorithms and their application in simulation platform for forging manipulator

Most researches focused on the analytical stabilized algorithm for the modular simulation of single domain, e.g., pure mechanical systems. Only little work has been performed on the problem of multi-domain simulation stability influenced by algebraic loops. In this paper, the algebraic loop problem is studied by a composite simulation method to reveal the internal relationship between simulation stability and system topologies and simulation unit models. A stability criterion of multi-domain composite simulation is established, and two algebraic loop compensation algorithms are proposed using numerical iteration and approximate function in multi-domain simulation. The numerical stabilized algorithm is the Newton method for the solution of the set of nonlinear equations, and it is used here in simulation of the system composed of mechanical system and hydraulic system. The approximate stabilized algorithm is the construction of response surface for inputs and outputs of unknown unit model, and it is utilized here in simulation of the system composed of forging system, mechanical and hydraulic system. The effectiveness of the algorithms is verified by a case study of multi-domain simulation for forging system composed of thermoplastic deformation of workpieces, mechanical system and hydraulic system of a manipulator. The system dynamics simulation results show that curves of motion and force are continuous and convergent. This paper presents two algorithms, which are applied to virtual reality simulation of forging process in a simulation platform for a manipulator, and play a key role in simulation efficiency and stability.

Optimum selection of mechanism type for heavy manipulators based on particle swarm optimization method

The mechanism type plays a decisive role in the mechanical performance of robotic manipulators. Feasible mechanism types can be obtained by applying appropriate type synthesis theory, but there is still a lack of effective and efficient methods for the optimum selection among different types of mechanism candidates. This paper presents a new strategy for the purpose of optimum mechanism type selection based on the modified particle swarm optimization method. The concept of sub-swarm is introduced to represent the different mechanisms generated by the type synthesis, and a competitive mechanism is employed between the sub-swarms to reassign their population size according to the relative performances of the mechanism candidates to implement the optimization. Combining with a modular modeling approach for fast calculation of the performance index of the potential candidates, the proposed method is applied to determine the optimum mechanism type among the potential candidates for the desired manipulator. The effectiveness and efficiency of the proposed method is demonstrated through a case study on the optimum selection of mechanism type of a heavy manipulator where six feasible candidates are considered with force capability as the specific performance index. The optimization result shows that the fitness of the optimum mechanism type for the considered heavy manipulator can be up to 0.578 5. This research provides the instruction in optimum selection of mechanism types for robotic manipulators.

A Kind of Kinematically Redundant Planar Parallel Manipulator for Optimal Output Accuracy

Theoretically, parallel manipulators perform higher precision than their serial counterparts. However, the output accuracy is sensitive to their configurations and dimensions. This paper presents a kind of parallel manipulator with kinematically redundant structure, which can improve the output accuracy by optimizing the error transmission from the active joints to the end-effector. With the kinematic redundancy, free redundant variables can be defined as second task variables, which provide the possibility to select a proper configuration for least error transmission at any pose (the position and orientation) of the end-effector for a given task. Contrast to non-redundant manipulators, the output errors of the proposed manipulator, caused by the active joints input errors, can be optimized rather than determined. By this goal, new limbs with redundant parallel structures are introduced to non-redundant planar parallel manipulators. Numerical example shows that the new architecture has the potential to enhance the output accuracy for a given pose or prescribed trajectory of the end-effector.Copyright

Performance Analysis of a Forging Manipulator Based on the Composite Modeling Method

This paper presents the performance analysis of one type of forging manipulator based on a new approach for the calculation of Jacobian matrices. The Jacobian matrix based evaluation criterions in robotics literature are studied to characterize the kinematic and dynamic manipulability, as well as the force capability of the studied manipulator. The performance measures with respect to the joint space are illustrated to describe the kinematic and dynamic capability of the manipulator intuitively. The ellipses at the best condition points are obtained. The research in this paper can be served as fundamentals of design and optimization of forging manipulators, and predict the best work conditions.

An analytical representation of conformal mapping for genus-zero implicit surfaces and its application to surface shape similarity assessment

This paper develops an analytical representation of conformal mapping for genus-zero implicit surfaces based on algebraic polynomial functions, and its application to surface shape similarity assessment. Generally, the conformal mapping often works as a tool of planar or spherical parameterization for triangle mesh surfaces. It is further exploited for implicit surface matching in this study. The method begins with discretizing one implicit surface by triangle mesh, where a discrete harmonic energy model related to both the mesh and the other implicit surface is established based on a polynomial-function mapping. Then both the zero-center constraint and the landmark constraints are added to the model to ensure the uniqueness of mapping result with the Mobius transformation. By searching optimal polynomial coefficients with the Lagrange-Newton method, the analytical representation of conformal mapping is obtained, which reveals all global and continuous one-to-one correspondent point pairs between two implicit surfaces. Finally, a shape similarity assessment index for (two) implicit surfaces is proposed through calculating the differences of all the shape index values among those corresponding points. The proposed analytical representation method of conformal mapping and the shape assessment index are both verified by the simulation cases for the closed genus-zero implicit surfaces. Experimental results show that the method is effective for genus-zero implicit surfaces, which will offer a new way for object retrieval and manufactured surface inspection. We develop an analytical representation of conformal mapping for implicit surfaces.An analytical conformal mapping describes a continuous one-to-one correspondence.Conformal mappings from complex surfaces to simple ones are effectively obtained.Conformal mappings between two similar complex surfaces are effectively obtained.

Prediction of Forming Limit Diagram for Seamed Tube Hydroforming Based on Thickness Gradient Criterion

This study establishes the forming limit diagram (FLD) for QSTE340 seamed tube hydroforming by finite element method (FEM) simulation. FLD is commonly obtained from experiment, theoretical calculation and FEM simulation. But for tube hydroforming, both of the experimental and theoretical means are restricted in the application due to the equipment costs and the lack of authoritative theoretical knowledge. In this paper, a novel approach of predicting forming limit using thickness gradient criterion (TGC) is presented for seamed tube hydroforming. Firstly, tube bulge tests and uniaxial tensile tests are performed to obtain the stress-strain curve for tube three parts. Then one FE model for a classical tube free hydroforming and another FE model for a novel experimental apparatus by applying the lateral compression force and the internal pressure are constructed. After that, the forming limit strain is calculated based on TGC in the FEM simulation. Good agreement between the simulation and experimental results is indicated. By combining the TGC and FEM, an alternative way of predicting forming limit with enough accuracy and convenience is provided.

Modeling and experimental validation of friction self-piercing riveted aluminum alloy to magnesium alloy

Friction self-piercing riveting (F-SPR) process has been proposed to achieve crack-free joining of low-ductility materials by combining SPR process with the concept of friction stir processing. The inhibition of cracking in an F-SPR joint is related to the in-process temperature as well as plastic deformation of materials, which are controlled by the process parameters, i.e., spindle speed and feed rate. However, the relationship between F-SPR process parameters and the temperature characteristics within the joint has not been established. In the current study, a coupled thermal-mechanical model based on solid mechanics was setup to study the F-SPR process of aluminum alloy and magnesium alloy. Temperature and strain rate-dependent material models and preset crack surface method were integrated in the model and geometry comparisons were conducted for model validation. Based on this model, the evolutions of temperature and plastic deformation in the rivet and the sheets of an F-SPR joint were obtained to reveal the formation mechanism of the joint. The temperature distribution and evolution of the sheet materials were correlated with F-SPR process parameters, and a critical spinning speed of 2000xa0rpm at a feed rate of 1.35xa0mm/s was determined capable of inhibiting cracking in the magnesium sheet.