The existing researches on singularity of parallel mechanism are mostly limited to the property and regularity of singularity locus and there is no further research into the geometric relationship between uncontrolled...The existing researches on singularity of parallel mechanism are mostly limited to the property and regularity of singularity locus and there is no further research into the geometric relationship between uncontrolled kinematic screw and parallel mechanism in singularity. A 3UPS-S parallel mechanism is presented which fulfils 3-DOF in rotation. The regularity of nutation angle singularity is analyzed based on the Jacobian matrix, and the singularity surface of 3UPS-S parallel mechanisms is obtained. By applying the concept of reciprocal product in screw theory, the singular kinematic screw is derived when 3UPS-S parallel mechanism is in singularity. The geometric relationship between singular kinematic screw and singular configuration of 3UPS-S parallel mechanism is investigated by using programs in MATLAB. It is revealed that there are two kinds of situation. Firstly, the three limbs of 3UPS-S parallel mechanism intersect the singular kinematic screw in space simultaneously; Secondly, two limbs cross the singular kinematic screw while the third limb parallels with that screw. It is concluded that the nutation angle singularity of 3UPS-S parallel mechanism belongs to the singular linear complexes. This paper sheds light into and clarifies the geometric relationship between singular kinematic screw and singular configuration of 3UPS-S parallel mechanism.展开更多
Recently, [1] presented an algorithm for rational matrix multiplication, in which the number of operators needed for carrying out the product of n×m and m×l rational matrices is 0(m(n+l)). The authors of [1]...Recently, [1] presented an algorithm for rational matrix multiplication, in which the number of operators needed for carrying out the product of n×m and m×l rational matrices is 0(m(n+l)). The authors of [1] claimed that their algorithm, at least theoretically, is optimal. In this report, we show that the conclusion of [1] is not true since the computational complexity of an operation depends on the word length of operands. If one accepts the view point of [1], then by inserting zeros and cutting digits, we can present an even 'efficient' algorithm for matrix multiplication, which only needs one multiplication展开更多
基金supported by Aeronautical Science Foundation of China(Grant No.20081651025)
文摘The existing researches on singularity of parallel mechanism are mostly limited to the property and regularity of singularity locus and there is no further research into the geometric relationship between uncontrolled kinematic screw and parallel mechanism in singularity. A 3UPS-S parallel mechanism is presented which fulfils 3-DOF in rotation. The regularity of nutation angle singularity is analyzed based on the Jacobian matrix, and the singularity surface of 3UPS-S parallel mechanisms is obtained. By applying the concept of reciprocal product in screw theory, the singular kinematic screw is derived when 3UPS-S parallel mechanism is in singularity. The geometric relationship between singular kinematic screw and singular configuration of 3UPS-S parallel mechanism is investigated by using programs in MATLAB. It is revealed that there are two kinds of situation. Firstly, the three limbs of 3UPS-S parallel mechanism intersect the singular kinematic screw in space simultaneously; Secondly, two limbs cross the singular kinematic screw while the third limb parallels with that screw. It is concluded that the nutation angle singularity of 3UPS-S parallel mechanism belongs to the singular linear complexes. This paper sheds light into and clarifies the geometric relationship between singular kinematic screw and singular configuration of 3UPS-S parallel mechanism.
文摘Recently, [1] presented an algorithm for rational matrix multiplication, in which the number of operators needed for carrying out the product of n×m and m×l rational matrices is 0(m(n+l)). The authors of [1] claimed that their algorithm, at least theoretically, is optimal. In this report, we show that the conclusion of [1] is not true since the computational complexity of an operation depends on the word length of operands. If one accepts the view point of [1], then by inserting zeros and cutting digits, we can present an even 'efficient' algorithm for matrix multiplication, which only needs one multiplication
