Type synthesis of 1T2R and 2R1T parallel mechanisms employing conformal geometric algebra

Song, Yimin; Han, Pengpeng; Wang, Panfeng

doi:10.1016/j.mechmachtheory.2017.11.009

Cited by 37 publications

(8 citation statements)

References 22 publications

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“…At the same time, Selig also proposed a method using an eight-dimensional algebra to build rigid body dynamics, and he claimed that inertias, velocities, and momenta all can be represented as the elements of that algebra and all the relationships between physical quantities could be given by the standard operations [38]. After that, attentions start to be paid by researchers in the robotic fields and amount of work has been done based on Clifford algebra [39,40], such as the forward and inverse position kinematics [41][42][43][44], singularity analysis [45,46], robot POC representation [47], type synthesis of parallel mechanisms [48], dynamics [49], freedom or constraint analysis [50][51][52], first-order kinematics and grub jobs [53]. As far as we know, the research of higher-order kinematics of parallel mechanisms based on CGA is relatively rare.…”

Section: •3•mentioning

confidence: 99%

Higher-Order Kinematics Modeling of 3-RRS Parallel Mechanism Based on CGA

Wang¹,

Zhao²,

E³

et al. 2020

Preprint

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Higher-order kinematics of mechanisms has been applied in servo motor control, human-robot interaction and machinery life design fields, etc. The representations of acceleration and jerk by screws have been fully developed by researchers with the methods of the differential of the matrix representation of SE(3) group. Clifford algebra, which is tighter and with higher computational efficiency than the matrix method, is another representation of the motions of rigid bodies. It has been used in position kinematics, grub task motion planning, and robot vision for its convenience of geometric representations and calculations. As far as we know, the work of higher-order kinematics of mechanisms based on Clifford algebra is rare. First, after recalling the based theory of motion representation in conformal geometric algebra (CGA), the mathematical relationships between flag and motor are built. Second, a method for the higher-order kinematics modeling of serial chain mechanisms is proposed. Finally, the higher-order kinematics of the 3-RRS parallel mechanism is built to prove the correctness of the algorithm. This work further enriches the application of CGA for the higher-order kinematics modeling of parallel mechanisms.

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Section: •3•mentioning

confidence: 99%

Higher-Order Kinematics Modeling of 3-RRS Parallel Mechanism Based on CGA

Wang¹,

Zhao²,

E³

et al. 2020

Preprint

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“…Sun and Huo [16] proposed a configuration method based on finite helix theory to solve the problem of motion restriction taking 1T2R parallel mechanism with accompanying motion as an example. Song et al [17] proposed a synthesis method for 1T2R parallel mechanism based on the conformal geometric algebra theory and obtained configuration layout of the limbs and joints of the robots. Xie et al [18] designed the configuration of 2T1R parallel manufacturing robot based on motion and constraint theory.…”

Section: Introductionmentioning

confidence: 99%

Type Synthesis Based on Modular Combination with Virtual Rotation Center and Application

Zhang

Yang

et al. 2022

International Journal of Rotating Machinery

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Type synthesis of mechanical structure is of great significance to the realization of mechanism target function, systematization, and stability of mechanical device. The type synthesis method of multilinkage robot has been given high demands with increasing number of degrees of freedom and high flexibility in special occasions. In order to improve the workspace and flexibility of mechanism, this paper studies the existing type synthesis theory and proposes a type synthesis method of modular combination with virtual rotation centers. Firstly, modular units are built. Secondly, modular units are expanded according to the needed paths. In the end, the expanded modular units are combined to form the kinematic linkages. Based on the proposed method, the configuration design of the aerial working platform and the self-adaptive levelling platform is completed. The stabilities of two platforms are checked by modal analysis. The prototype products are manufactured, respectively, for further verifying validity of the method. The designed aerial working platform with virtual rotation centers can achieve 360° rotating large workspace, more compact mechanical structure, and short arrival time at the same height than the common scissor-type and mast-type aerial working platforms. The designed adaptive levelling platform is tested that ensures the levelling of the upper surface at different inclinations. The method can provide new idea for the mechanism configuration and expand the application scope of new mechanisms.

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“…Many recent researches have concentrated on PU-and P * U * -equivalent PMs. For PU-equivalent PMs, Fan et al [26] presented a type synthesis method based on the integration of configuration evolution and Lie group theory, and obtained many PU-equivalent PMs like PU-PRC-UPS; Song et al [27] proposed an analytical method based on conformal geometrical algebra to synthesize 2R1T and 1T2R PMs, and obtained some novel PU-equivalent PMs like 2RPUR-RPU; Xu et al [28] synthesized the 2R1T PMs with two continuous rotational axes according to four spatial arrangements cases of constraint forces, and obtained several PU-equivalent PMs such as PU-RPU-UPS; Liu et al [29] presented a novel 3-RRPRR 2R1T PM without parasitic motion and developed its variants, but two rotational axes are on the middle plane, which means that they cannot be categorized as PU-equivalent PMs. For P * U * -equivalent PMs, to describe the finite motion algebraically and perform systematically type synthesis are extremely difficult, and most novel P * U * -equivalent PMs are inspired by the typical 3-RPS PM [17][18][19] or designed by rule of thumb [30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Constraint characteristics and type synthesis of two families of 1T2R parallel mechanism

Meng

et al. 2022

Robotica

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PU- and P*U*-equivalent parallel mechanisms (PMs) are critical families of PMs with one translational and two rotational (1T2R) degree of freedoms and have always been a research hotspot among lower mobility PMs. However, researches on these two families of PMs remain to be inadequate, and existing types are few and uncomprehensive. In this study, first, general wrench systems of PU-equivalent are derived based on virtual-chain approach and screw theory, revealing its constraint characteristics under general configuration. Cause of one parasitic motion is put forward and general wrench systems of P*U*-equivalent PMs with one parasitic motion are obtained. In addition, constraint analysis has been carried out to figure out constraint characteristics of P*U*-equivalent PMs with three parasitic motions. Second, branch chains are divided by generating constraints, and their structures are synthesized based on the presented rules. Then, the process for type synthesis of PU-equivalent PMs and P*U*-equivalent PMs and a series of novel 1T2R PMs are attained based on this. Finally, a novel PU-equivalent PM, 2PRU-PRUPc, and a novel P*U*-equivalent PM with one parasitic motion, 2PRU-PUU PM, are analyzed, demonstrating the effectiveness of the proposed type synthesis method.

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Type synthesis of 1T2R and 2R1T parallel mechanisms employing conformal geometric algebra

Cited by 37 publications

References 22 publications

Higher-Order Kinematics Modeling of 3-RRS Parallel Mechanism Based on CGA

Higher-Order Kinematics Modeling of 3-RRS Parallel Mechanism Based on CGA

Type Synthesis Based on Modular Combination with Virtual Rotation Center and Application

Constraint characteristics and type synthesis of two families of 1T2R parallel mechanism

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