Singularity analysis of a 3-RPS parallel manipulator using geometric algebra

Li, Qinchuan; Xiang, Ji’nan; Chai, Xinxue; Chen, Wu

doi:10.3901/cjme.2015.0728.103

Cited by 19 publications

(9 citation statements)

References 19 publications

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“…6. These configurations are similar to RO-type singularity that classified in Zlatanov et al (2002) and Li et al (2015). For the double triangular mechanism, the inverse singularity is identified by using the Jacobian matric J C to solve the following equation:…”

Section: Velocity Model and Singular Configurations Of The Mechanismmentioning

confidence: 74%

Kinematic analysis and evaluation of a hybrid mechanism for computer assisted bone reduction surgery

Phu

Essomba²,

Idram

et al. 2019

Mech. Sci.

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In severe fracture cases, a bone can be separated into two fragments and it is mandatory to reposition the bone fragments together. This type of surgery is called "bone reduction surgery". Originally, the operation consisted in manipulating the bones fragments by hand in open surgery. The most advanced technique relies on robotic manipulators providing higher precision and stability. A new mechanical architecture is proposed based on a 3-RPS tripod parallel mechanism combined with a Double Triangular Planar parallel mechanism. Its kinematic and velocity models are calculated and the parasitic motion generated by the tripod mechanism is considered in the final result. The workspace it can generate is compared to the Stewart manipulator, which is a classical mechanism for the targeted application. The use of a robotic manipulator is due to be part of an entire surgical procedure involving a pre-operative simulation software dedicated to pre-planning reduction surgery, namely PhysiGuide. It is used to measure the kinematic associated with bone fragments manipulation and transfer it to the robot during the intra-operative phase. Simulations are then performed based on a real patient's fracture images showing the suitability of the present mechanism with bone reduction surgery.S. Nguyen Phu et al.: A hybrid mechanism for bone reduction surgery

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Section: Velocity Model and Singular Configurations Of The Mechanismmentioning

confidence: 74%

Kinematic analysis and evaluation of a hybrid mechanism for computer assisted bone reduction surgery

Phu

Essomba²,

Idram

et al. 2019

Mech. Sci.

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“…Tanev (2006Tanev ( , 2008 proposed a methodology of geometric algebra for identifying the singularity configurations for lower-mobility parallel mechanisms. Zhang (2008) and Li et al (2015) studied the singularity of 3-RPS parallel mechanism using geometric algebra. Yao et al (2017) applied geometric algebra to discussing the singularity of over-constrained 3-RPR parallel mechanisms with general and special structures.…”

Section: Introductionmentioning

confidence: 99%

“…There are no literatures on the singularity of six-DOF parallel mechanisms studied by geometric algebra. Reference to Tanev (2006Tanev ( , 2008, Li et al (2015) and Yao et al (2017), this paper presents the geometric algebra approach to obtaining the singularity loci of the six-DOF parallel mechanisms of 6-UPS and 6-PUS. The remainder of this paper is organized as follows: Section 2, necessary knowledge of geometric algebra used in this paper are introduced.…”

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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“…Tanev was the first to use GA to analyze the singularities of a limited–degree of freedom PM. Li et al extended his work to study the singularities of a 3‐RPS PM. Moreover, conformal GA, which is a special case of GA, was used by Kim et al to analyze the singularity of a redundant PM.…”

Section: Introductionmentioning

confidence: 99%

Singularity analysis of the 3/6 Stewart parallel manipulator using geometric algebra

Chen

Yao

et al. 2018

Math Methods in App Sciences

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Singularity analysis of a parallel manipulator (PM) is important in its trajectory planning and workspace design. This paper presents a new method based on geometric algebra (GA) for the singularity analysis of the 3/6‐SPS Gough‐Stewart PM, where S denotes a spherical joint and P a prismatic pair. The 6 line vectors associated with the SPS limb are expressed using GA. An analytic singular polynomial is then derived as the coefficient of the outer product of all 6 line vectors. This polynomial provides an overall description of the singularity of the 3/6‐SPS Gough‐Stewart PM. Position‐singularity loci and orientation‐singularity loci can be drawn based on this polynomial, the latter of which have seldom been addressed. It is also shown that the proposed GA‐based method is geometrically intuitive and computationally efficient.

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Singularity analysis of a 3-RPS parallel manipulator using geometric algebra

Cited by 19 publications

References 19 publications

Kinematic analysis and evaluation of a hybrid mechanism for computer assisted bone reduction surgery

Kinematic analysis and evaluation of a hybrid mechanism for computer assisted bone reduction surgery

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

Singularity analysis of the 3/6 Stewart parallel manipulator using geometric algebra

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