Position analysis in polynomial form of planar mechanisms with Assur groups of class 3 including revolute and prismatic joints

Mitsi, S.; Bouzakis, K.‐D.; Mansour, Gabriel; Popescu, Iulian

doi:10.1016/s0094-114x(03)00090-9

Cited by 25 publications

(21 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Now, let us suppose that all link dimensions remain unaltered, that is, s 5,9 ′ = s 5,9 , s 6,9 ′ = s 6,9 , s 7,9 ′′ = s 7,9 , and s 8,9 ′′ = s 8,9 , and the orientation of the slider joint is fixed with respect to its adjacent links such that α 1 = π − arctan 5 2 and α 3 = 2π − arctan 5 3 . Then, given the orientations of △P 5 P 6 P 9 ′ and △P 7 P 8 P 9 ′′ , it turns out that α 2 = π − arctan 2 3 and α 4 = 2π − arctan 1 2 .…”

Section: Replacing One Revolute Jointmentioning

confidence: 99%

“…The position analysis problem of the ten 5-link Assur kinematic chains was solved for the first time in closed form by Li and Matthew in [8]. Other solutions for 5-link Assur kinematic chains have been presented, at least, in [9,10,11,12,13]. An extensive research on the position analysis of Assur kinematic chains with only revolute joints, i.e.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Formulating Assur kinematic chains as projective extensions of Baranov trusses

Rojas

Thomas

2012

Mechanism and Machine Theory

View full text Add to dashboard Cite

The real roots of the characteristic polynomial of a planar linkage determine its assembly modes. In this work it is shown how the characteristic polynomial of a Baranov truss derived using a distance-base formulation contains all the necessary and sufficient information for solving the position analysis of the Assur kinematic chains resulting from replacing some of its revolute joints by slider joints. This is a relevant result because it avoids the case-by-case treatment that requires new sets of variable eliminations to obtain the characteristic polynomial of each Assur kinematic chain.

show abstract

Section: Replacing One Revolute Jointmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Formulating Assur kinematic chains as projective extensions of Baranov trusses

Rojas

Thomas

2012

Mechanism and Machine Theory

View full text Add to dashboard Cite

show abstract

“…However, their kinematic analysis -one of the most important aspects in linkage design -is still to be solved for more convenience and for greater effectiveness. And yet a lot of work has been done [2][3][4][5][6][7][8][9][10]. Kinematic analysis includes position analysis, velocity analysis and acceleration analysis; of these, position analysis is the most difficult.…”

Section: Introductionmentioning

confidence: 99%

“…Kinematic analysis includes position analysis, velocity analysis and acceleration analysis; of these, position analysis is the most difficult. To analyze the position of a complex planar linkage, there are two categories of methods: the global method [9,10] and the group method [2,[4][5][6][7][8]. The global method takes the linkage as a whole by listing the position equations based on the vector loop, and solving the equations using different techniques.…”

Section: Introductionmentioning

confidence: 99%

Position analysis of higher-class Assur groups by virtual variable searching and its application in a multifunction domestic sewing machine

Zhang

Zou

Guo

2005

Int J Adv Manuf Technol

View full text Add to dashboard Cite

This paper presents a simple and effective method to solve the position of higher-class Assur groups by means of virtual variable searching. It transforms the higher-class Assur groups into a constraint link, Class II Assur group(s), and virtual driving link(s), defined by the virtual variable. The constraint link is reassembled by one-dimensional searching of the virtual variable, and the potential solutions of the position of the higher-class Assur group are achieved with rapid mathematic convergence. Detailed criteria are set up for complicated higherclass Assur groups, including how to select the virtual driving link and constraint Link, and how to decide the solving sequence of converted Class II Assur groups. A versatile visual program has been developed to simulate higher-class planar mechanisms. Finally, an example of the feeding mechanism of a multifunction domestic sewing machine demonstrates the new method.

show abstract

“…In 1996, Merlet tackled the same problem from a different point of view which resulted in a case-by-case analysis [3]. Other solutions for some 5-link Assur kinematic chains have been presented, at least, in [4], [5], [6], [7]. The development of a remarkable unified formulation for the forward kinematics of all fully-parallel planar robots started in 1995 with Husty's first use of the Grünwald-Blaschke kinematic mapping to solve the forward kinematics of the 3-RPR robot [8].…”

mentioning

confidence: 99%

The Univariate Closure Conditions of All Fully Parallel Planar Robots Derived From a Single Polynomial

Rojas

Thomas

2013

IEEE Trans. Robot.

View full text Add to dashboard Cite

Abstract-The real roots of the univariate polynomial closure condition of a planar parallel robot determine the solutions of its forward kinematics. This paper shows how the univariate polynomials of all fullyparallel planar robots can be derived directly from that of the widely known 3-RPR robot by simply formulating these polynomials in terms of distances and oriented areas. This is a relevant result because it avoids the case-by-case treatment that requires different sets of variable eliminations to obtain the univariate polynomial of each fully-parallel planar robot.

show abstract

Position analysis in polynomial form of planar mechanisms with Assur groups of class 3 including revolute and prismatic joints

Cited by 25 publications

References 6 publications

Formulating Assur kinematic chains as projective extensions of Baranov trusses

Formulating Assur kinematic chains as projective extensions of Baranov trusses

Position analysis of higher-class Assur groups by virtual variable searching and its application in a multifunction domestic sewing machine

The Univariate Closure Conditions of All Fully Parallel Planar Robots Derived From a Single Polynomial

Contact Info

Product

Resources

About