Decomposition of Planar Burmester Problems Using Kinematic Mapping

Ge, Q. J.; Zhao, Ping; Purwar, Anurag

doi:10.1007/978-3-319-00398-6_11

Cited by 8 publications

(4 citation statements)

References 8 publications

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“…For the attitude issues in the motion synthesis of mechanisms, Han et al [17] proposed a rigid body guidance method of bar mechanism based on solution domain synthesis, and the designed linkage mechanism could accurately achieve the given attitude conditions. Yang et al [18] applied a four-position solution domain synthesis method to the dimensional synthesis of the Watt-I six-bar mechanism. Ge et al [19][20][21] proposed a new algorithm for mechanism synthesis based on kinematic mapping and conducted dimension and type syntheses at the same time, which improved the accuracy of the synthesis of a linkage mechanism.…”

Section: Introductionmentioning

confidence: 99%

Kinematic synthesis and simulation of a vegetable pot seedling transplanting mechanism with four exact task poses

Sun¹,

Xu²,

Zhou³

et al. 2023

International Journal of Agricultural and Biological Engineering

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To obtain a picking and planting integrated transplanting mechanism (PITM) with ideal trajectory shape, reasonable operating attitude, and compact structure for vegetable pot seedling transplanting, a symmetrical structural PITM composed of two planetary carriers and driven by a cam-noncircular gear combination mechanism was proposed in this paper. In accordance with the requirements of transplanting agronomy, the shape of the motion trajectory and the attitude of the end tip of the clamping claw at several specific positions (the starting and end points of picking seedling, the starting point of pushing seedling, and a special point on the return segment) were planned. To make the clamping claws of PITM pass through a set of prescribed positions, the mechanism was simplified to an open-chain 3R mechanism. An accurate four-position-based method for solving the open-chain mechanism model was adopted to obtain the curves of its fixed hinge point (central point) and dynamic hinge point (circle point). The ratio of adjacent bars' lengths was analyzed to determine the feasible interval of the central and circle point curves and the reasonable link length. A desired closed transplanting trajectory that goes through the given points and the corresponding transmission ratio model of the open-chain mechanism was established. After the transmission ratio of each stage of gear and cam pairs was calculated and distributed, the prototype of PITM was designed and manufactured. Lastly, the effectiveness and feasibility of the design were verified through a preliminary experiment of the prototype.

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Section: Introductionmentioning

confidence: 99%

Kinematic synthesis and simulation of a vegetable pot seedling transplanting mechanism with four exact task poses

Sun¹,

Xu²,

Zhou³

et al. 2023

International Journal of Agricultural and Biological Engineering

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show abstract

“…McCarthy and Soh (2011) introduced the methods of perpendicular bisector constraint and dyad triangle for planar mechanism dimensional synthesis. Zhao et al (2016) and Ge et al (2013) explored the use of kinematic mapping in dimensional synthesis. Han and Qian (2009), Bai et al (2016) and Glabe and McCarthy (2019) also investigated the synthesis of planar mechanisms.…”

Section: Introductionmentioning

confidence: 99%

Motion generation of a planar 3R serial chain based on conformal geometric algebra with applications to planar linkages

Wang

Sun

et al. 2022

Mech. Sci.

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Abstract. A planar three-revolute (3R) serial chain is an important part of many mechanisms. The classical approach in motion generation of a planar 3R serial chain is to construct closed-loop equations based on complex numbers, which yields a large-scale polynomial system. In this study, a new approach of planar 3R serial chain motion generation by establishing the relative kinematics model based on conformal geometric algebra (CGA) is proposed. The simpler design equations are obtained, which can be used to design a planar 3R serial chain that can accurately achieve the N poses. In the numerical examples, the number of different poses is used to verify the correctness and efficiency of the proposed method by using polyhedral homotopy continuation. The results indicate that the design equations obtained via CGA are more concise for improving the solving efficiency compared with the previous method. Finally, a geared five-bar mechanism with a seven-pose motion generation example is considered.

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“…One prominent example is the projectivized dual quaternion model of SE (3), which exhibits particularly nice geometric and algebraic properties. [1][2][3][4] In the past, it has been successfully employed at several occasions for the synthesis of linkages, [5][6][7][8][9][10] for their analysis, [11][12][13][14][15] or simply for general studies of space kinematics. [16][17][18] A crucial ingredient in all of these investigations is the concept of constraint varieties.…”

Section: Introductionmentioning

confidence: 99%

The kinematic image of RR, PR, and RP dyads

Rad¹,

Scharler²,

Schröcker³

2018

Robotica

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We provide necessary and sufficient conditions for admissible transformations in the projectivised dual quaternion model of rigid body displacements and we characterise constraint varieties of dyads with revolute and prismatic joints in this model. Projective transformations induced by coordinate changes in moving and/or fixed frame fix the quadrics of a pencil and preserve the two families of rulings of an exceptional three-dimensional quadric. The constraint variety of a dyad with two revolute joints is a regular ruled quadric in a three-space that contains a "null quadrilateral". If a revolute joint is replaced by a prismatic joint, this quadrilateral collapses into a pair of conjugate complex null lines and a real line but these properties are not sufficient to characterise such dyads. We provide a complete characterisation by introducing a new invariant, the "fiber projectivity", and we present examples that demonstrate its potential to explain hitherto not sufficiently well understood phenomena.

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Decomposition of Planar Burmester Problems Using Kinematic Mapping

Cited by 8 publications

References 8 publications

Kinematic synthesis and simulation of a vegetable pot seedling transplanting mechanism with four exact task poses

Kinematic synthesis and simulation of a vegetable pot seedling transplanting mechanism with four exact task poses

Motion generation of a planar 3R serial chain based on conformal geometric algebra with applications to planar linkages

The kinematic image of RR, PR, and RP dyads

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