A Finite and Instantaneous Screw Based Approach for Topology Design and Kinematic Analysis of 5-Axis Parallel Kinematic Machines

Sun, Tao; Yang, Shuofei; Huang, Tian; Dai, Jian S.

doi:10.1186/s10033-018-0241-6

Cited by 40 publications

(20 citation statements)

References 36 publications

(56 reference statements)

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“…Whereas for a PM, the finite screw of its moving platform can be obtained as the intersection of finite screws of all the limbs. Under the guidance of these principles, a synthesis method based on the finite screw has been proposed and applied to the type synthesis of 3T PMs [56], 3T1R PMs with a variable rotational axis [57], 2T3R PMs [58], and 1T2R PMs [59]. This method mainly has two features.…”

Section: Finite Screw Methodsmentioning

confidence: 99%

“…The investigation on systematic type synthesis approaches of lower mobility PMs dates back to the last century and has experienced a gold period with great progress at the beginning of this century. Based on various mathematical tools, a variety of approaches have been presented in the literature, including the Lie group theory-based method [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], the method based on G F (generalized function) sets [30][31][32][33][34][35], linear transformation method [36][37][38][39][40][41][42][43][44][45][46], position and orientation characteristic (POC) set method [47][48][49][50][51][52], finite screw method [53][54][55][56][57][58][59], screw theory-based method …”

Section: Introductionmentioning

confidence: 99%

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Type Synthesis of Lower Mobility Parallel Mechanisms: A Review

2019

Chin. J. Mech. Eng.

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Type synthesis of mechanisms aims to systematically determine all possible structures for a specific mobility requirement. Numerous methods based on different theories were proposed for type synthesis of lower mobility parallel mechanisms in past decades. However, there does not exist a comprehensive review on these approaches. Therefore, the goal of this paper is to give such a review, classifying the approaches proposed in the literature into three groups, namely, motion-based methods, constraint-based methods, and other methods. The motion-based methods include the Lie group based method, the G F set method, the linear transformation method, the POC set method, and the finite screw method. The constraint-based methods involve the screw theory-based method, the virtual chain method, the method based on Grassmann line geometry and line graphs, and the motion constraint generator method. Other methods contain the enumeration approach based on the general CGK mobility formula and the graph theory method. Upon thoroughly analyzing the characteristics and/or limitations of each method, this review provides a well reference to help researchers find an effective synthesis method for innovative design and further scientific investigations for mechanisms.

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Section: Finite Screw Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Type Synthesis of Lower Mobility Parallel Mechanisms: A Review

2019

Chin. J. Mech. Eng.

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“…Li et al [20,21] presented the type synthesis of parallel mechanisms according to screw theory and Lie group. Sun et al [22,23] proposed a generalized method to solve inverse kinematics of serial and parallel mechanisms using finite screw. Gabardi et al [24] investigated the kinematics analysis of a 4-UPU fully parallel manipulator and performed the analysis of actuation Jacobian, constraint Jacobian, and singularity configurations by screw theory.…”

Section: •3•mentioning

confidence: 99%

“…Firstly, the velocity and acceleration vectors of motion pairs of the equivalent series joints can be calculated based on Eqs. (22) and (23). Then, by applying Eqs.…”

Section: Forward Kinematics Analysis Of Hybrid Mechanismsmentioning

confidence: 99%

Generalized Kinematics Analysis of Hybrid Mechanisms Based on Screw Theory and Lie Groups Lie Algebras

Sun

Chen

et al. 2020

Preprint

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The advanced mathematical tools are used to conduct research on the kinematics analysis of hybrid mechanisms, and the generalized analysis method and concise kinematics transfer matrix are obtained. First, according to the kinematics analysis of serial mechanisms, the basic principles of Lie groups Lie algebras in dealing with the spatial switching and differential operations of screw vectors are briefly explained. Then, based on the standard ideas of Lie operations, the method for kinematics analysis of parallel mechanisms is derived, and Jacobian matrix and Hessian matrix are formulated both recursively and in closed form. After that, according to the mapping relationship between the parallel joints and the corresponding equivalent series joints, a forward kinematics analysis method and two inverse kinematics analysis methods of hybrid mechanisms are studied. A case study is performed to verify the calculated matrices, in which a humanoid hybrid robotic arm with the parallel-series-parallel configuration is taken as an example. Simulation experiment results show that the obtained formulas are exact and the proposed method for kinematics analysis of hybrid mechanisms is practicable.

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“…Some high-end machining centers have 5-axis or 6-axis process capability with 2 or 3 dimensional rotational DOFs [1]. However, most of the 5-axis and 6-axis machining centers at present suffer from a common disadvantage that relatively small rotational angles, which restricts the work performance.…”

Section: Introductionmentioning

confidence: 99%

Design and analysis of a class of redundant collaborative manipulators with 2D large rotational angles

et al. 2019

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The parallel spindle heads with high rotational capability are demanded in the area of multi-axis machine tools and 3D printers. This paper focuses on designing a class of 2R1T (R: Rotation; T: Translation) parallel spindle heads and the corresponding collaborative 5-axis manipulators with 2-dimension (2D) large rotational angles. In order to construct 2D rotational degrees of freedom (DOFs), a platform with 2D revolute joints is proposed first. Based on the constraint screw theory, the feasible limbs that can be connected in the platform are synthesized. In order to provide constant rotational axis for the platform, a class of redundant limbs are designed. A class of redundant 2R1T parallel spindle heads is obtained by connecting the redundant limbs with the platform and the redundant characteristics are verified by the modified Grübler-Kutzbach criterion. The corresponding 5-axis collaborative manipulators are presented by constructing a 2-DOF series translational bottom moving platform. The inverse kinematics and the orientation workspace as well as the decoupling characteristics of this type of 2R1T parallel spindle heads are analyzed. The results show that these manipulators have large 2D rotational angles than the traditional A3/Z3 heads and can be potentially used in the application of multi-axis machine tools and the 3D printers.

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A Finite and Instantaneous Screw Based Approach for Topology Design and Kinematic Analysis of 5-Axis Parallel Kinematic Machines

Cited by 40 publications

References 36 publications

Type Synthesis of Lower Mobility Parallel Mechanisms: A Review

Type Synthesis of Lower Mobility Parallel Mechanisms: A Review

Generalized Kinematics Analysis of Hybrid Mechanisms Based on Screw Theory and Lie Groups Lie Algebras

Design and analysis of a class of redundant collaborative manipulators with 2D large rotational angles

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