Singularity analysis of a four degree-of-freedom parallel manipulator based on an expanded 6×6 Jacobian matrix

Choi, Hee-Byoung; Ryu, Jeha

doi:10.1016/j.mechmachtheory.2012.06.008

Cited by 30 publications

(18 citation statements)

References 17 publications

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“…The forward and inverse kinematics of the HCL bearing can be simplified by noting that translational displacements along the X and Y axes are negligible [3,24]. Thus, only one translational DOF, combined with three rotational degrees of freedom, need to be solved: translation along the Z-axis, pitch rotation, flap rotation, and lead-lag rotation.…”

Section: Methodsmentioning

confidence: 99%

Real-time estimation of helicopter blade kinematics using integrated linear displacement sensors

Allred¹,

Jolly²,

Buckner³

2015

Aerospace Science and Technology

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Section: Methodsmentioning

confidence: 99%

Real-time estimation of helicopter blade kinematics using integrated linear displacement sensors

Allred¹,

Jolly²,

Buckner³

2015

Aerospace Science and Technology

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“…33 The linear dependency of J a can be used to analyze constraint singularity. 34 For the mechanism, three cases will be discussed in the following section. In this case, n 1 is parallel to n 2 , the vectors n 1 and n 2 are parallel or perpendicular to the plane O-XY synchronously.…”

Section: Singularity Affected By Augmented Jacobian Matrixmentioning

confidence: 99%

Type synthesis and kinematics analysis of a family of three translational and one rotational pick-and-place parallel mechanisms with high rotational capability

Zhang

Liu

et al. 2019

Advances in Mechanical Engineering

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This article proposes a family of spatial three translational and one rotational parallel mechanisms (PMs) for pick-andplace operation. Their features are one independent rotation of the mechanism with four identical limbs, which are provided by the four revolute joints on the moving platform. The rotational capability of the PMs has a range of at least 180°. This article focuses on the synthesis of the PMs and kinematics analysis of the 4-P(2-SS)R parallel mechanism. First, based on the Lie group theory, three parallelograms are used in designing the PMs. The limbs are listed and two types of three translational and one rotational PMs are synthesized. Then, a typical 4-P(2-SS)R PM is selected, the 6 3 6 Jacobian matrix and the 6 3 6 3 6 Hessian matrix of the mechanism are derived for solving the displacement, velocity, and acceleration of the mechanism. Finally, singularity configurations are disclosed from the 6 3 6 Jacobian matrix, and the workspace of the mechanism is provided to illustrate the high rotational capability.

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“…Choi and Ryu compared and discuss the 6 x 6 and 4x4 Jacobian matrices and suggested to expanding 6 x 6 Jacobian matrices for H4 parallel manipulator (3T and 1R vertical axis). From the expansion of the Jacobian matrix for 4 DOF [22], three distinct restricted singularities can be acquired.…”

Section: Parallel Manipulatormentioning

confidence: 99%

An Application of Jacobian Matrix in Kinematic of Multi-loop Spatial Mechanism

2019

IJITEE

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Mechanism is an intended to turn input motion into a required set of output motion and forces. Now a days the spatial mechanism is widely used in various industrial applications like parallel kinematic machines as a robot manipulator. The main aim of the review paper is to use the Jacobian matrix into the kinematic analysis. From the review papers analysis, it has been concluded that the Kinematic analysiswith help of Jacobian matrix performed various Multi-loop Spatial Mechanism settings for Kinematic geometry, its topology and to carried out displacement modelling. It also used to Kinematic Design, synthesis and optimization. Finally, Comparison of existing methods for Kinematic Singularities with Jacobian in Parallel Manipulator.

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Singularity analysis of a four degree-of-freedom parallel manipulator based on an expanded 6×6 Jacobian matrix

Cited by 30 publications

References 17 publications

Real-time estimation of helicopter blade kinematics using integrated linear displacement sensors

Real-time estimation of helicopter blade kinematics using integrated linear displacement sensors

Type synthesis and kinematics analysis of a family of three translational and one rotational pick-and-place parallel mechanisms with high rotational capability

An Application of Jacobian Matrix in Kinematic of Multi-loop Spatial Mechanism

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