Mapping Matrix

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Sungchul Kang - One of the best experts on this subject based on the ideXlab platform.

  • design of a static balancing mechanism for a serial manipulator with an unconstrained joint space using one dof gravity compensators
    IEEE Transactions on Robotics, 2014
    Co-Authors: Changhyun Cho, Sungchul Kang
    Abstract:

    We propose a design method for a gravity compensator using unit spring balancers for multi-degree-of-freedom (DOF) and multilink manipulators. Existing spring balancers can be applied to a new design of a gravity compensator. When applying spring balancers to a new gravity compensator, it is necessary to determine how many spring balancers are required and where they should be placed. Our proposed design method can determine the number of spring balancers and their locations. In this study, the design of a spring balancer for multi-DOF and multilink manipulators is considered as a Mapping between two spaces (i.e., the joint space for gravitational torques and the spring balancer space to compensate torques). The Mapping Matrix is obtained through eigenvalue analyses of the potential energy function. The number of rows of the Mapping Matrix represents the number of unit gravity compensators. The row vector of the Mapping Matrix also indicates the locations of the unit gravity compensators. Examples are presented to validate the effectiveness of the proposed method.

  • IROS - Design of a static balancing mechanism with unit gravity compensators
    2011 IEEE RSJ International Conference on Intelligent Robots and Systems, 2011
    Co-Authors: Changhyun Cho, Sungchul Kang
    Abstract:

    This paper proposes a design method of a static balancing mechanism using unit gravity compensators (e.g., 1-dof gravity compensator). In the design of a multi-dofs static balancing mechanism it is necessary to determine how many springs (or unit gravity compensators) are required and where they should be placed. This problem can be overcome by computing the Mapping Matrix between the joint space and gravity compensator space. The Mapping Matrix is obtained by analyses of the potential energy function. The number of rows of the Mapping Matrix indicates the amount of unit gravity compensators and linear joint constraints representing locations of unit gravity compensators. Example studies are presented to verify the effectiveness of the proposed method. Simulations are performed in that static balancing mechanisms designed by the proposed method can counterbalance the gravitational torques completely.

Changhyun Cho - One of the best experts on this subject based on the ideXlab platform.

  • URAI - Design method of a planar static balancer using a motion Matrix
    2017 14th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI), 2017
    Co-Authors: Sang-hyung Kim, Changhyun Cho
    Abstract:

    This paper presents a design method of a static balancer using a motion Matrix, which represents possible joint motions of a target mechanism. When the space Mapping method is applied, several computations (e.g., partial differentiation of the potential energy function and decomposition of eigenvalues) are necessary. We suggest a design method that the Mapping Matrix of the space Mapping method is derived from the motion Matrix with no computations. The motion Matrix is determined from the concept of mobility and connectivity. The motion Matrix is modified in the viewpoint of static balancing to obtain the Mapping Matrix. It is also shown that a Mapping Matrix is generated by combining motion matrices. The proposed design method using the motion Matrix is verified with planar mechanisms.

  • Design of a static balancer with equivalent Mapping
    Mechanism and Machine Theory, 2016
    Co-Authors: Changhyun Cho, Woosub Lee
    Abstract:

    Abstract This paper proposes a design method of a static balancer with multi-dof unit gravity compensators. The design method based on the space Mapping method is extended to a multi-dof gravity compensator space. A multi-dof gravity compensator can be equivalently represented with one-dof gravity compensators applying the design method. An equivalent Mapping Matrix is determined between rotation angles of a multi-dof gravity compensator and those of one-dof gravity compensators. That is, characteristics of a multi-dof gravity compensator are described in the one-dof gravity compensator space. Complexity and variety originated from the multi-dof can be overcome using the equivalent Mapping Matrix during designing a static balancer with multi-dof gravity compensators. The design of a static balancer with multi-dof gravity compensators is conducted: 1. perform the design only with the one-dof gravity compensator space to determine the base Mapping Matrix between the joint and the one-dof gravity compensator space, 2. applying the equivalent Mapping Matrix to the base Mapping Matrix. Various designs are obtained. Results of simulations show that the total potential energy is invariant for all poses.

  • design of a static balancing mechanism for a serial manipulator with an unconstrained joint space using one dof gravity compensators
    IEEE Transactions on Robotics, 2014
    Co-Authors: Changhyun Cho, Sungchul Kang
    Abstract:

    We propose a design method for a gravity compensator using unit spring balancers for multi-degree-of-freedom (DOF) and multilink manipulators. Existing spring balancers can be applied to a new design of a gravity compensator. When applying spring balancers to a new gravity compensator, it is necessary to determine how many spring balancers are required and where they should be placed. Our proposed design method can determine the number of spring balancers and their locations. In this study, the design of a spring balancer for multi-DOF and multilink manipulators is considered as a Mapping between two spaces (i.e., the joint space for gravitational torques and the spring balancer space to compensate torques). The Mapping Matrix is obtained through eigenvalue analyses of the potential energy function. The number of rows of the Mapping Matrix represents the number of unit gravity compensators. The row vector of the Mapping Matrix also indicates the locations of the unit gravity compensators. Examples are presented to validate the effectiveness of the proposed method.

  • IROS - Design of a static balancing mechanism with unit gravity compensators
    2011 IEEE RSJ International Conference on Intelligent Robots and Systems, 2011
    Co-Authors: Changhyun Cho, Sungchul Kang
    Abstract:

    This paper proposes a design method of a static balancing mechanism using unit gravity compensators (e.g., 1-dof gravity compensator). In the design of a multi-dofs static balancing mechanism it is necessary to determine how many springs (or unit gravity compensators) are required and where they should be placed. This problem can be overcome by computing the Mapping Matrix between the joint space and gravity compensator space. The Mapping Matrix is obtained by analyses of the potential energy function. The number of rows of the Mapping Matrix indicates the amount of unit gravity compensators and linear joint constraints representing locations of unit gravity compensators. Example studies are presented to verify the effectiveness of the proposed method. Simulations are performed in that static balancing mechanisms designed by the proposed method can counterbalance the gravitational torques completely.

Dachang Zhu - One of the best experts on this subject based on the ideXlab platform.

  • Optimal design method for 3-DOF planar compliant mechanisms based on Mapping Matrix constraints
    Structures, 2020
    Co-Authors: Wanghu Zhan, He Xianghua, Yang Jiamou, Lai Junhao, Dachang Zhu
    Abstract:

    Abstract The Mapping Matrix cannot be given in advance when using traditional topology optimization method (TOM) to design compliant mechanism (CM), which makes the CM unable to accurately establish model and affects the mechanism precise control. In this paper, a design method for CM is proposed based on planar parallel prototype mechanism with optimal structural parameters, the Mapping Matrix under the optimal structural parameter reasonably modified as the desired Mapping Matrix of CM in the process of topology optimization. Based on the idea of linear regression, the difference between the actual Mapping Matrix of the CM and the expected Mapping Matrix is constrained to makes the actual Mapping Matrix of the CM approach the expected Mapping Matrix gradually in the optimization process, take the low order modal frequency of the mechanism as objective, and finally obtains the CM that meets the design requirements. Experimental and simulation results show that take the Mapping Matrix as constraint in CM design process can achieve the consistency of differential motion between the CM and the parallel prototype mechanism within a range of deviation, which indicates that the method is effective for the design of CM and provides a foundation for the follow-up research of CM.

  • Topology optimization of a 6-DOF spatial compliant mechanism based on Stewart propotype platform
    Acta Mechanica Sinica, 2019
    Co-Authors: Dachang Zhu, Wanghu Zhan
    Abstract:

    To improve the global stiffness and conveniently build a model of a compliant mechanism with spatial multiple degrees of freedom (DOF), the topology optimization method, combined with the isomorphic Mapping Matrix, is proposed in this paper for structure synthesis of a 6-DOF spatial compliant mechanism. By using the differential approximation method, the Jacobian Matrix of the Stewart prototype platform is calculated as the isomorphic Mapping Matrix, and its eigenvalues and eigenvectors are considered. Combining the isomorphic Mapping Matrix with the solid isotropic material with the penalization topology optimization method, the topological model of the 6-DOF spatial compliant mechanism is constructed, and a topological structure of the 6-DOF spatial compliant mechanism is derived which has the same differential kinematic characteristics as the Gough–Stewart prototype platform. Piezoelectric actuators are mounted inside the topological structure during the three-dimensional printing manufacturing process, and its driver directions are in accordance with the driver configuration directions of the Gough–Stewart prototype platform. The effectiveness of the proposed method for topological structure synthesis of the 6-DOF spatial compliant mechanism is demonstrated through several numerical examples and experimental studies.

  • Topology Optimization of Spatially Compliant Mechanisms with an Isomorphic Matrix of a 3-UPC Type Parallel Prototype Manipulator.
    Micromachines, 2018
    Co-Authors: Dachang Zhu, Wanghu Zhan, Alessandro Simeone
    Abstract:

    A novel topology optimization approach is proposed in this paper for the design of three rotational degree-of-freedom (DOF) spatially compliant mechanisms, combining the Jacobian isomorphic Mapping Matrix with the solid isotropic material with penalization (SIMP) topological method. In this approach, the isomorphic Jacobian Matrix of a 3-UPC (U: universal joint, P: prismatic joint, C: cylindrical joint) type parallel prototype manipulator is formulated. Subsequently, the orthogonal triangular decomposition and differential kinematic method is applied to uncouple the Jacobian Matrix to construct a constraint for topology optimization. Firstly, with respect to the 3-UPC type parallel prototype manipulator, the Jacobian Matrix is derived to map the inputs and outputs to be used for initializing the topology optimization process. Secondly, the orthogonal triangular decomposition with the differential kinematic method is used to reconstruct the uncoupled Mapping Matrix to derive the 3-UPC type parallel prototype manipulator. Finally, a combination of the solid isotropic material with penalization (SIMP) method and the isomorphic Mapping Matrix is applied to construct the topological model. A typical three rotational DOF spatially compliant mechanism is reported as a numerical example to demonstrate the effectiveness of the proposed method.

  • Topology Optimization of 3-DOF Peristaltic Structure Robot Based on Vector Continuous Mapping Matrix
    Mathematical Problems in Engineering, 2016
    Co-Authors: Gao Wang, Dachang Zhu, Ning Liu
    Abstract:

    A mechanism for topology optimization of 3-DOF parallel peristaltic structure robot with vector continuous Mapping Matrix using Solid Isotropic Material with Penalization (SIMP) method is presented in this paper. We focus on how to prevent the differential motion consistency between parallel prototype mechanisms with peristaltic structure. As the conventional parallel robot joints/hinges are no longer needed after topology optimization, therefore, we renamed this kind of 3-DOF robot structures as peristaltic structure. In the proposed method, the vector continuous Mapping Matrix is built as stress/strain transfer direction conditions for topology optimization of peristaltic structure, and SIMP method is used for multi-inputs and multioutputs decided by parallel prototype mechanisms. Some numerical examples are presented to illustrate the validity of the proposed method.

Li Chen - One of the best experts on this subject based on the ideXlab platform.

  • a unified framework for decomposition of design structure Matrix and domain Mapping Matrix
    Design Automation Conference, 2008
    Co-Authors: Simon Li, Li Chen
    Abstract:

    In literature, design structure Matrix (DSM), which is a square Matrix, has been widely used to address single-domain dependency relationships (e.g., product architecture, process workflow, and organization structure). To extend the DSM efforts, a rectangular Matrix becomes a logical format to capture and analyze cross-domain dependency relationships, namely, domain Mapping Matrix (DMM) [1]. In this context, this paper proposes a unified framework for decomposition of DSM and DMM. The unified framework consists of four methodological phases to offer the functions of DSM clustering, DSM sequencing, and DMM decomposition. To support the development of this framework, various decomposition-related techniques from applied mathematics and engineering design are reviewed. Three Matrix examples have been used to illustrate the framework’s applicability.Copyright © 2008 by ASME

Daosen Zhai - One of the best experts on this subject based on the ideXlab platform.

  • Adaptive Codebook Design and Assignment for Energy Saving in SCMA Networks
    IEEE Access, 2017
    Co-Authors: Daosen Zhai
    Abstract:

    Sparse code multiple access (SCMA) has been proposed as a candidate air interface (AI) technique for 5G wireless networks. However, the existing resource management schemes with predesigned SCMA codebooks cannot fully exploit user diversities in the frequency domain, thus degrading the performance of SCMA systems. To fully exploit the potential of SCMA, in this paper, we design a more flexible and configurable SCMA through adaptively adjusting the codebook design and assignment according to the user's features. Specifically, for the uplink networks, first we formulate a detection complexity minimization problem by jointly considering the codebook design (i.e., Mapping Matrix and constellation graph design) and codebook assignment, which is an integer linear program and NP-hard in general. To tackle this hard problem effectively, first we borrow the idea of dual coordinate search to devise a suboptimal but computational efficient algorithm to determine the Mapping Matrix and codebook assignment. Based on the obtained Mapping Matrix, we use the multi-dimensional modulation characteristic of SCMA to carefully design the constellations for each codebook to further reduce the detection complexity. For the downlink networks, we formulate a total power consumption minimization problem by jointly considering the codebook design and assignment and power allocation. Exploiting the special structure of the problem, we employ the Lagrangian dual decomposition technique to propose a fast iterative algorithm, which can solve the problem optimally with low complexity. Finally, we present extensive simulations to exhibit the performance improvement against other algorithms in terms of detection complexity and power consumption. The modified SCMA in this paper can be intelligently optimized based on service and user awareness, which can provide some guidelines for the design of software-defined AI in future wireless networks.

  • VTC Fall - Joint Codebook Design and Assignment for Detection Complexity Minimization in Uplink SCMA Networks
    2016 IEEE 84th Vehicular Technology Conference (VTC-Fall), 2016
    Co-Authors: Daosen Zhai, Min Sheng, Xijun Wang
    Abstract:

    To improve the spectrum efficiency (SE), sparse code multiple access (SCMA) has been proposed as an candidate for 5G wireless networks. Although SCMA has good SE performance, it suffers from high detection complexity, which may degrade its energy efficiency (EE) performance. To make up for this deficiency, we in this paper jointly consider codebook design (i.e., Mapping Matrix and constellation graph design) and codebook assignment to investigate the detection complexity minimization problem for uplink SCMA networks. To tackle this hard problem effectively, we first borrow the idea of dual coordinate search to devise a cost-efficient algorithm to determine the Mapping Matrix and codebook assignment. Based on the Mapping Matrix, we exploit the multi-dimensional modulation characteristic of SCMA to carefully design the constellations for each codebook to further reduce the detection complexity. Finally, we present some simulations to illustrate the performance gain of our proposed algorithm as compared with other schemes.