Forward Kinematics of Casing Oscillator

Nam, Yoon Kwon; Park, Myeong-Kwan

doi:10.1109/tmech.2006.882997

Cited by 4 publications

(6 citation statements)

References 9 publications

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“…This becomes clear if we consider the physical meaning of Eq. (12). This equation can be obtained by constraining the length and direction of D 1 D 2 .…”

Section: Discussion About the Real Rootsmentioning

confidence: 99%

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A Geometric Approach to Obtain the Closed-Form Forward Kinematics of H4 Parallel Robot

Liu

Kong

Wan

et al. 2018

Journal of Mechanisms and Robotics

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To obtain the closed-form forward kinematics of parallel robots, researchers use algebra-based method to transform and simplify the constraint equations. However, this method requires a complicated derivation that leads to high-order univariate variable equations. In fact, some particular mechanisms, such as Delta, or H4 possess many invariant geometric properties during movement. This suggests that one might be able to transform and reduce the problem using geometric approaches. Therefore, a simpler and more efficient solution might be found. Based on this idea, we developed a new geometric approach called geometric forward kinematics (GFK) to obtain the closed-form solutions of H4 forward kinematics in this paper. The result shows that the forward kinematics of H4 yields an eighth degree univariate polynomial, compared with earlier reported 16th degree. Thanks to its clear physical meaning, an intensive discussion about the solutions is presented. Results indicate that a general H4 robot can have up to eight nonrepeated real solutions for its forward kinematics. For a specific configuration of H4, the nonrepeated number of real roots could be restricted to only two, four, or six. Two traveling plate configurations are discussed in this paper as two typical categories of H4. A numerical analysis was also performed for this new method.

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“…This becomes clear if we consider the physical meaning of Eq. (12). This equation can be obtained by constraining the length and direction of D 1 D 2 .…”

Section: Discussion About the Real Rootsmentioning

confidence: 99%

“…By translating the forearms to the center of the traveling plate, the forward kinematics can be reduced to a simpler geometric problem, which involves finding the center from three known points on a sphere. Other successful applications of the geometric approach include a casing oscillator [12] and a special Stewart platform [13].…”

Section: Introductionmentioning

confidence: 99%

A Geometric Approach to Obtain the Closed-Form Forward Kinematics of H4 Parallel Robot

Liu

Kong

Wan

et al. 2018

Journal of Mechanisms and Robotics

View full text Add to dashboard Cite

show abstract

“…Similar approach has been found in various other works [17,18] wherein the degree of univariate polynomial has been reduced to lower the computational complexity. Geometrical arguments [19][20][21][22][23] have been helpful in determining the maximum number of the platform poses and definite formulation of FK problem. FK analysis of a 3-dof parallel robot which is a part of 5-dof reconfigurable robot has been presented in [24].…”

Section: Analytical Approachesmentioning

confidence: 99%

“…are the outputs from the fuzzy model for the same pth input data. Output of the fuzzy model can be calculated using (21), where 'i,' (i = 1,..,n) is the number of inference rules, k, (k = 1,..,4) is the number of input variables to the fuzzy model, l ik is the position of the centre of the peak and σ ik is the width of the Gaussian activation function for ith rule and kth input. As defined previously, y ij is the consequent part of the fuzzy rulebase, a is a positive constant and e is the Euler's number.…”

Section: Problem Formulationmentioning

confidence: 99%

Forward kinematics modelling of a parallel ankle rehabilitation robot using modified fuzzy inference

Jamwal

Xie

Tsoi

et al. 2010

Mechanism and Machine Theory

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“…Generally in practical control and other applications a unique solution of FK is required and various numerical approaches (Deshmukh and Michael 1990) to solve non-linear equations can be used for this purpose. Several researchers have been able to linearize few of the non linear equations obtained from the kinematic analysis or have been able to reduce the degree of the set of polynomial equations (Nam and Park 2004). The system of equations of reduced order has further been solved using one of the numerical methods.…”

Section: Forward Kinematicsmentioning

confidence: 99%