Inverse kinematics and geometric singularity analysis of a 3-SPS/S redundant motion mechanism using conformal geometric algebra

Kim, Je Seok; Jeong, Jin Han; Park, Jahng Hyon

doi:10.1016/j.mechmachtheory.2015.02.009

Cited by 43 publications

(19 citation statements)

References 19 publications

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“…The alternative multi-section designs can be structures such as given in Woehrmann et al (2013) with effective magnetic actuation and interleaved continuum-rigid manipulators as presented in Conrad et al (2013). Moreover, a non-compliant but similar structure to the mechanism proposed in this paper, known as 3-SPS mechanism is studied in Alici and Shirinzadeh (2004) and Kim et al (2015).…”

Section: Introductionmentioning

confidence: 99%

Design and Modelling of a Cable-Driven Parallel-Series Hybrid Variable Stiffness Joint Mechanism for Robotics

Yiğit

Boyraz

2017

Mech. Sci.

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Abstract. The robotics, particularly the humanoid research field, needs new mechanisms to meet the criteria enforced by compliance, workspace requirements, motion profile characteristics and variable stiffness using lightweight but robust designs. The mechanism proposed herein is a solution to this problem by a parallel-series hybrid mechanism. The parallel term comes from two cable-driven plates supported by a compression spring in between. Furthermore, there is a two-part concentric shaft, passing through both plates connected by a universal joint. Because of the kinematic constraints of the universal joint, the mechanism can be considered as a serial chain. The mechanism has 4 degrees of freedom (DOF) which are pitch, roll, yaw motions and translational movement in z axis for stiffness adjustment. The kinematic model is obtained to define the workspace. The helical spring is analysed by using Castigliano's Theorem and the behaviour of bending and compression characteristics are presented which are validated by using finite element analysis (FEA). Hence, the dynamic model of the mechanism is derived depending on the spring reaction forces and moments. The motion experiments are performed to validate both kinematic and dynamic models. As a result, the proposed mechanism has a potential use in robotics especially in humanoid robot joints, considering the requirements of this robotic field.

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Section: Introductionmentioning

confidence: 99%

Design and Modelling of a Cable-Driven Parallel-Series Hybrid Variable Stiffness Joint Mechanism for Robotics

Yiğit

Boyraz

2017

Mech. Sci.

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“…According to (8), we can readily obtain However, due to the volume sign of the tetrahedron B 1 B 2 B 3 B 4 , it will lead to the symmetric extraneous roots with respect to the plane B 1 B 2 B 3 if we obtain the coordinateinvariant equation only from (17). In order to avoid the extraneous roots, we will use its volume of the tetrahedron B 1 B 2 B 3 B 4 to geometrically model the direct kinematics of 6-4 Stewart platforms.…”

Section: The Derivation Of the Coordinate-invariant Polynomial Equationmentioning

confidence: 99%

“…In recent decades, CGA has been mostly applied to solve the inverse kinematics problem of the serial mechanisms [11][12][13][14] via CGA operation of the geometric entities. In addition, Tanev [15,16], Kim et al [17], and Huo et al [18] employed CGA to study the singularity analysis of PMs. Huo et al [18] and Li et al [19] proposed a mobility analysis approach for PMs based on geometric algebra.…”

Section: Introductionmentioning

confidence: 99%

A Geometric Modeling and Computing Method for Direct Kinematic Analysis of 6-4 Stewart Platforms

Zhang

Liu

Wei

et al. 2018

Mathematical Problems in Engineering

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A geometric modeling and solution procedure for direct kinematic analysis of 6-4 Stewart platforms with any link parameters is proposed based on conformal geometric algebra (CGA). Firstly, the positions of the two single spherical joints on the moving platform are formulated by the intersection, dissection, and dual of the basic entities under the frame of CGA. Secondly, a coordinate-invariant equation is derived via CGA operation in the positions of the other two pairwise spherical joints. Thirdly, the other five equations are formulated in terms of geometric constraints. Fourthly, a 32-degree univariate polynomial equation is reduced from a constructed 7 by 7 matrix which is relatively small in size by using a Gröbner-Sylvester hybrid method. Finally, a numerical example is employed to verify the solution procedure. The novelty of the paper lies in that (1) the formulation is concise and coordinate-invariant and has intrinsic geometric intuition due to the use of CGA and (2) the size of the resultant matrix is smaller than those existed.

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“…Yao et al (2017) applied geometric algebra to discussing the singularity of over-constrained 3-RPR parallel mechanisms with general and special structures. Additionally, Kim et al (2015) studied the singularities of a redundant motion parallel mechanism using conformal geometric algebra.…”

Section: Introductionmentioning

confidence: 99%

Geometric algebra approach to analyzing the singularity of six-DOF parallel mechanism

Cheng

2019

JAMDSM

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Singular configurations must be avoided in the practical manipulation of parallel mechanism. This paper presents an approach of singularities analysis of six degrees of freedom (DOF) parallel mechanism applying geometric algebra. Twists of all passive joints in each limb are described in geometric algebra while all the active joints are locked. And wrenches produced from each limb and acting on the moving platform are derived from the calculations of the outer product and its dual of the corresponding twists. The singular condition of parallel mechanism depends on whether the wrenches acting on the moving platform failed to constrain all the motions, which can be accomplished by the outer product with its duality followed. Two six-DOF parallel mechanisms 6-UPS and 6-PUS are introduced to verify the approach proposed in this paper. The results indicate that geometric algebra can also be used for singularity analysis of six-DOF parallel mechanism.

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Inverse kinematics and geometric singularity analysis of a 3-SPS/S redundant motion mechanism using conformal geometric algebra

Cited by 43 publications

References 19 publications

Design and Modelling of a Cable-Driven Parallel-Series Hybrid Variable Stiffness Joint Mechanism for Robotics

Design and Modelling of a Cable-Driven Parallel-Series Hybrid Variable Stiffness Joint Mechanism for Robotics

A Geometric Modeling and Computing Method for Direct Kinematic Analysis of 6-4 Stewart Platforms

Geometric algebra approach to analyzing the singularity of six-DOF parallel mechanism

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