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2023 1

2012 1

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assembly changing motions 1

cusp points 1

discriminant of repeated roots 1

diversity 1

marine environments 1

microorganism community 1

planar parallel manipulator 1

proteorhodopsin (PR) 1

quartic polynomial 1

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Diversity and distribution of proteorhodopsin-containing microorganisms in marine environments

Bo WEI

Frontiers of Environmental Science & Engineering 2012, Volume 6, Issue 1, Pages 98-106 doi: 10.1007/s11783-010-0278-y

Abstract: Proteorhodopsin (PR) is a recently discovered protein involved in the utilization of light energy.A better understanding of the ecological role of PR will help clarify the effect of the global flow ofProteorhodopsin (GDDP), as a tool for analyzing the diversity and distribution of PR-containing microorganismsRepresentative cases of the former include SAR11-PR and HOT2C01-PR.Interestingly, PR communities cluster by geographic locale but not by water depth.

Keywords： proteorhodopsin (PR) microorganism community diversity marine environments

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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