On the Special Bases of Two- and Three-Screw Systems

Tsai, Min-Chun; Lee, H. W.

doi:10.1115/1.2919223

Cited by 17 publications

(11 citation statements)

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“…Alternatively, they provided a consistent representation of screw systems in terms of an orthonormal basis of the orthogonal subspaces associated with screw systems under consideration. Tsai and Lee [15] presented a method to search the principal screws of a screw system based on the reduced echelon form of the screw matrix.…”

Section: Introductionmentioning

confidence: 99%

“…This article focuses on such an issue and presents an algebraic methodology to identify the principal screws and their pitches, which is much more easily understood and has better computational efficiency than that proposed in reference [5]. According to the reciprocal screw theory [1,2], the identifications of principal screws and principal pitches of a system whose order is larger than three can be equivalently transformed into the identifications of those of its reciprocal screw system whose order is less than three [1,2,13,15]. Consequently, this article only discusses the applications to the second-and third-order screw systems after the theoretical analysis of this method.…”

Section: Introductionmentioning

confidence: 99%

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An algebraic methodology to identify the principal screws and pitches of screw systems

Zhao

Zhou

Feng

et al. 2009

Proceedings of the Institution of Mechanical Engineers, Part C:

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This article investigates the principal screws and their pitches of screw systems from the viewpoint of line geometry. It starts from the fact that any n-independent screws pertaining to a specified n-screw system can be utilized to determine the system, and the pitch of a unit screw is the half of the reciprocal product with itself. The reciprocal product matrix of a screw matrix is therefore defined to determine the principal pitches and the directions of the principal screw axes of the system. With matrix diagonalization procedure, one can immediately obtain the principal pitches and the principal screws of a screw system. The whole procedure is straightforward and easily understood by an engineer with primary knowledge of linear algebra. Besides, the computational effort is greatly reduced and the efficiency is better compared with other methods. As a matter of fact, the pitch of any screw of a screw system can be represented by a homogeneous quadratic form of the linear combination coefficients. The homogeneous quadratic equation of the pitch of a screw system represents a conic curve in a two-system and an ellipsoid or a hyperboloid in a three-system. Therefore, this article also provides such visualizations of the principal axes in two-and three-dimensional spaces at last. Downloaded from Fig. 3 The h distribution with respect to k 1 and k 2 , and the contours in k 1 ok 2 -plane for equation (45) JMES1394

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An algebraic methodology to identify the principal screws and pitches of screw systems

Zhao

Zhou

Feng

et al. 2009

Proceedings of the Institution of Mechanical Engineers, Part C:

View full text Add to dashboard Cite

show abstract

“…Alternatively, they provided a consistent representation of screw systems in terms of an orthonormal basis of the orthogonal subspaces associated with the screw systems under consideration [7][8][9]. Tsai and Lee [12] presented a method to find the principal screws of a screw system based on the reduced echelon form of the screw matrix.…”

Section: Introductionmentioning

confidence: 99%

Identification of principal screws of two- and three-screw systems

Zhao

Chu

Feng

2007

Proceedings of the Institution of Mechanical Engineers, Part C:

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The current paper proposes a unified analytical methodology to identify the principal screws of two-and three-screw systems. Based on the definition of the pitch of a screw, it first obtains an identical homogeneous quadric equation. According to functional analysis theory, it is known that the partial derivatives of an identical quadric equation with respect to its variables must be zero. Therefore, the paper deduces a set of linear homogeneous equations that are made up of the partial derivatives of the quadric equation. With the existing criteria of nonzero solutions for homogeneous linear algebra equations, it ultimately obtains the formulas of the principal pitches and the associated principal screws of the system. The most outstanding contribution of this methodology is that it proposes a unified analytical approach to identify the principal pitches and the principal coordinate systems of the second-order and the thirdorder screw systems. This should be a new contribution to the screw theory and will boost its applications to the kinematics analysis of robots and spatial mechanisms.

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“…The two straight lines can also be obtained and proved by using another method proposed by form a set of new principal screws, which is just the seventh special three-system screws presented by Hunt (1978), Tsai and Lee (1993).…”

Section: Parallel Manipulators New Developments 362mentioning

confidence: 99%

“…Parkin (1990) specified the principal screws of the three-system from three given screws by adopting the mutual moment operation. Tsai & Lee (1993) studied the principal screws from three known screws by means of eigenvector. Zhang & Xu (1998) constructed the principal screws from three known screws by using algebraic method.…”

Section: Introductionmentioning

confidence: 99%