In parallel mechanisms, singular configurations (singularities) have to be avoided during motion. All the singularities should be located in order to avoid them. Hence, relationships involving all the singular platform poses (singularity locus) and the mechanism geometric parameters are useful in the design of parallel mechanisms. This paper presents a new expression of the singularity condition of the most general mechanism (6-6 FPM) of a class of parallel mechanisms usually named fully-parallel mechanisms (FPM). The presented expression uses the mixed products of vectors that are easy to be identified on the mechanism. This approach will permit some singularities to be geometrically found. A procedure, based on this new expression, is provided to transform the singularity condition into a ninth-degree polynomial equation whose unknowns are the platform pose parameters. This singularity polynomial equation is cubic in the platform orientation parameters and a sixth-degree one in the platform orientation parameters. Finally, how to derive the expression of the singularity condition of a specific FPM from the presented 6-6 FPM singularity condition will be shown along with an example.
Singularity-Locus expression of a class of parallel mechanisms
DI GREGORIO, Raffaele
2002
Abstract
In parallel mechanisms, singular configurations (singularities) have to be avoided during motion. All the singularities should be located in order to avoid them. Hence, relationships involving all the singular platform poses (singularity locus) and the mechanism geometric parameters are useful in the design of parallel mechanisms. This paper presents a new expression of the singularity condition of the most general mechanism (6-6 FPM) of a class of parallel mechanisms usually named fully-parallel mechanisms (FPM). The presented expression uses the mixed products of vectors that are easy to be identified on the mechanism. This approach will permit some singularities to be geometrically found. A procedure, based on this new expression, is provided to transform the singularity condition into a ninth-degree polynomial equation whose unknowns are the platform pose parameters. This singularity polynomial equation is cubic in the platform orientation parameters and a sixth-degree one in the platform orientation parameters. Finally, how to derive the expression of the singularity condition of a specific FPM from the presented 6-6 FPM singularity condition will be shown along with an example.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
