The paper discusses the analytical expressions of a motion profile characterized by elliptic jerk. This motion profile is obtained through a kinematic approach, defining the jerk profile and then obtaining acceleration, velocity, and displacement laws by successive integrations. A dimensionless formulation is adopted for the sake of generality. The main characteristics of the profile are analyzed, outlining the relationships between the profile parameters. A kinematic comparison with other motion laws is carried out: trapezoidal velocity, trapezoidal acceleration, cycloidal, sinusoidal jerk, and modified sinusoidal jerk. Then, the features of these motion profiles are evaluated in a dynamic case study, assessing the vibrations induced to a second-order linear system with different levels of damping. The results show that the proposed motion law provides a good compromise between different performance indexes (settling time, maximum absolute values of velocity and acceleration).

Analytical expression of motion profiles with elliptic jerk

Pietro Fanghella;Giovanni Berselli;Luca Bruzzone
2023-01-01

Abstract

The paper discusses the analytical expressions of a motion profile characterized by elliptic jerk. This motion profile is obtained through a kinematic approach, defining the jerk profile and then obtaining acceleration, velocity, and displacement laws by successive integrations. A dimensionless formulation is adopted for the sake of generality. The main characteristics of the profile are analyzed, outlining the relationships between the profile parameters. A kinematic comparison with other motion laws is carried out: trapezoidal velocity, trapezoidal acceleration, cycloidal, sinusoidal jerk, and modified sinusoidal jerk. Then, the features of these motion profiles are evaluated in a dynamic case study, assessing the vibrations induced to a second-order linear system with different levels of damping. The results show that the proposed motion law provides a good compromise between different performance indexes (settling time, maximum absolute values of velocity and acceleration).
File in questo prodotto:
File Dimensione Formato  
analytical-expression-of-motion-profiles-with-elliptic-jerk.pdf

accesso aperto

Tipologia: Documento in versione editoriale
Dimensione 1.08 MB
Formato Adobe PDF
1.08 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/1125775
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 3
social impact