A novel motion synthesis approach with expandable solution space for planar linkages based on kinematic-mapping

Zhao, Ping; Li, Xiangyun; Zhu, Lihong; Zi, Bin; Ge, Q. J.

doi:10.1016/j.mechmachtheory.2016.06.021

Cited by 30 publications

(14 citation statements)

References 9 publications

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“…(11) can be derived from these four relations, except that when p 2 p 5 p 8 ¼ 0, these four relations become necessary, but not a sufficient, conditions for Eq. (11). To sum up, Eq.…”

Section: Constraining a Spherical Pose With Spherical Dyadmentioning

confidence: 99%

“…It is easy to demonstrate the above four relations are equivalent to Eq. (11), meaning that the other five equations in Eq. (11) can be derived from these four relations, except that when p 2 p 5 p 8 ¼ 0, these four relations become necessary, but not a sufficient, conditions for Eq.…”

Section: Constraining a Spherical Pose With Spherical Dyadmentioning

confidence: 99%

“…11, except for the case that p 2 p 5 p 8 ¼ 0 and (12) are just necessary but not sufficient conditions for Eq. (11). To readily exclude those solutions, which satisfy Eq.…”

Section: Least-squaresmentioning

confidence: 99%

“…While the exact motion synthesis problem of four or five prescribed poses has been well studied, most of the current solutions to the synthesis of mechanisms for approximate motion (an arbitrary number of poses), however, require complex and time consuming algorithms. In our previous work, we proposed a simple and efficient algebraic method for planar four-bar linkages synthesis [9][10][11], which uncovers the geometric constraint hidden in the given motion via a linear, twostep method. During the synthesis process, kinematic mapping was employed to express the given motion and define the constraint equations.…”

Section: Introductionmentioning

confidence: 99%

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A Unified Approach to Exact and Approximate Motion Synthesis of Spherical Four-Bar Linkages Via Kinematic Mapping

Zhao

Purwar

et al. 2017

Journal of Mechanisms and Robotics

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This paper studies the problem of spherical four-bar motion synthesis from the viewpoint of acquiring circular geometric constraints from a set of prescribed spherical poses. The proposed approach extends our planar four-bar linkage synthesis work to spherical case. Using the image space representation of spherical poses, a quadratic equation with ten linear homogeneous coefficients, which corresponds to a constraint manifold in the image space, can be obtained to represent a spherical RR dyad. Therefore, our approach to synthesizing a spherical four-bar linkage decomposes into two steps. First, find a pencil of general manifolds that best fit the task image points in the least-squares sense, which can be solved using singular value decomposition (SVD), and the singular vectors associated with the smallest singular values are used to form the null-space solution of the pencil of general manifolds; second, additional constraint equations on the resulting solution space are imposed to identify the general manifolds that are qualified to become the constraint manifolds, which can represent the spherical circular constraints and thus their corresponding spherical dyads. After the inverse computation that converts the coefficients of the constraint manifolds to the design parameters of spherical RR dyad, spherical four-bar linkages that best navigate through the set of task poses can be constructed by the obtained dyads. The result is a fast and efficient algorithm that extracts the geometric constraints associated with a spherical motion task, and leads naturally to a unified treatment for both exact and approximate spherical motion synthesis.

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“…(11) can be derived from these four relations, except that when p 2 p 5 p 8 ¼ 0, these four relations become necessary, but not a sufficient, conditions for Eq. (11). To sum up, Eq.…”

Section: Constraining a Spherical Pose With Spherical Dyadmentioning

confidence: 99%

Section: Constraining a Spherical Pose With Spherical Dyadmentioning

confidence: 99%

“…11, except for the case that p 2 p 5 p 8 ¼ 0 and (12) are just necessary but not sufficient conditions for Eq. (11). To readily exclude those solutions, which satisfy Eq.…”

Section: Least-squaresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Unified Approach to Exact and Approximate Motion Synthesis of Spherical Four-Bar Linkages Via Kinematic Mapping

Zhao

Purwar

et al. 2017

Journal of Mechanisms and Robotics

Self Cite

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show abstract

“…Hayes and Zsombor-Murrary [5] and Hayes and Rucu [6] developed a uniform polynomial system for integrated type and dimensional synthesis of planar dyads for rigid body guidance. Zhao et al [7,8] presented a kinematic mapping based algorithm to the simultaneous type and dimensional synthesis of planar four-bar and sixbar mechanisms. In their work, the motion of four-bar coupler are viewed as being subject to three kinds of geometric constraints: a point of the coupler staying on a circle, a point of the coupler staying on a line, and a line of the coupler staying tangent to a circle; these three constraints are mechanically realizable by RR dyad, PR dyad, and RP dyad, respectively.…”

Section: Introductionmentioning

confidence: 99%

A Line Geometric Approach to Kinematic Acquisition of Geometric Constraints of Planar Motion

Wu¹,

et al. 2017

Journal of Mechanisms and Robotics

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This paper examines the problem of geometric constraints acquisition of planar motion through a line-geometric approach. In previous work, we have investigated the problem of identifying point-geometric constraints associated with a motion task which is given in a parametric or discrete form. In this paper, we seek to extend the point-centric approach to the line-centric approach. The extracted geometric constraints can be used directly for determining the type and dimensions of a physical device such as mechanical linkage that generates this constrained motion task.

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Structural-Parametric Synthesis of Planar Motion Generating Mechanisms and Manipulators

Baigunchekov,

Laribi,

Carbone

et al. 2024

Mechanisms and Machine Science

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A novel motion synthesis approach with expandable solution space for planar linkages based on kinematic-mapping

Cited by 30 publications

References 9 publications

A Unified Approach to Exact and Approximate Motion Synthesis of Spherical Four-Bar Linkages Via Kinematic Mapping

A Unified Approach to Exact and Approximate Motion Synthesis of Spherical Four-Bar Linkages Via Kinematic Mapping

A Line Geometric Approach to Kinematic Acquisition of Geometric Constraints of Planar Motion

Structural-Parametric Synthesis of Planar Motion Generating Mechanisms and Manipulators

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