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CA50 1

DME 1

EGR 1

HCCI engine 1

PRR 1

assembly changing motions 1

combustion 1

cusp points 1

discriminant of repeated roots 1

planar parallel manipulator 1

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Cusp points and assembly changing motions in the PRR-PR-PRR planar parallel manipulator

Frontiers of Mechanical Engineering 2023, Volume 18, Issue 2, doi: 10.1007/s11465-022-0743-x

Abstract: Most parallel manipulators have multiple solutions to the direct kinematic problem. The ability to perform assembly changing motions has received the attention of a few researchers. Cusp points play an important role in the kinematic behavior. This study investigates the cusp points and assembly changing motions in a two degrees of freedom planar parallel manipulator. The direct kinematic problem of the manipulator yields a quartic polynomial equation. Each root in the equation determines the assembly configuration, and four solutions are obtained for a given set of actuated joint coordinates. By regarding the discriminant of the repeated roots of the quartic equation as an implicit function of two actuated joint coordinates, the direct kinematic singularity loci in the joint space are determined by the implicit function. Cusp points are then obtained by the intersection of a quadratic curve and a cubic curve. Two assembly changing motions by encircling different cusp points are highlighted, for each pair of solutions with the same sign of the determinants of the direct Jacobian matrices.

Keywords： planar parallel manipulator assembly changing motions cusp points quartic polynomial discriminant of repeated roots

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Numerical study of EGR effects on reducing the pressure rise rate of HCCI engine combustion

Gen CHEN, Norimasa IIDA, Zuohua HUANG,

Frontiers in Energy 2010, Volume 4, Issue 3, Pages 376-385 doi: 10.1007/s11708-010-0118-6

Abstract: of thermal ignition preparation extends non-linearly; peak values of pressure, pressure rising rate (PRRMoreover, maximum PRR decreases as CA50 is retarded.Maximum PRR is almost constant with the fixed CA50 despite the change in EGR ratio, indicating that the

Keywords： HCCI engine combustion EGR DME CA50 PRR