Only *square matrices* have *inverses.* Additionally, *the Determinant* is _only_ defined for *square matrices.* Since the Jacobian Matrices, in many of these examples, start out as NOT SQUARE in the FIRST place, it *finally* becomes apparent that *Robot Arm singularity* and whether or not the associated Jacobian Matrix _ITSELF_ is *singular* (i.e. possesses a Matrix Inverse) are two TOTALLY DIFFERENT *versions* of the meaning of *singular.* In many videos, the circumstance of *Robot Arm singularity* is simply defined as the moment when the Jacobian Matrix exhibits a ZERO VALUE for the calculation of its associated Determinant. Since only *square matrices* can even HAVE a Determinant, *^this^ choice* for defining the condition of *Robot Arm singularity* (which is the "habit" of many _other_ videos on this topic) would seem to be a deficient choice. Your choice, for defining the condition of *Robot Arm singularity,* by defining it as the *group of Robot Arm JOINT ANGLES* that causes a value of Jacobian Matrix *rank* to occur THAT IS *less than* the *MAXIMUM rank* possible (exhibited at _some_ particular grouping of Robot Arm JOINT ANGLES) would seem to be a *far superior Definition* for the *mathematical* onset of the circumstance of *Robot Arm singularity.*
The book also mentions the singularities occur when the Jacobian matrix's rank drops from its maximal rank which is the general case. When the Jacobian matrix is square (i.e. a special case), the shortcut is to check its determinant. I prefer to go with the rank's notion.
This reminds me of school, I'd just sit and look at the teacher. With absolutely no idea what they are talking about, or even why they are talking at all. At least I know why this guy is talking 😐.
Great explanation professor! the examples in the end helped tremendously!
I'm way too stupid to be watching this video lmao
Yea lol. I came here because I heard about singularities in my robotics workshop and this dude hits me with the Jacobian matrix.
Only *square matrices* have *inverses.* Additionally, *the Determinant* is _only_ defined for *square matrices.* Since the Jacobian Matrices, in many of these examples, start out as NOT SQUARE in the FIRST place, it *finally* becomes apparent that *Robot Arm singularity* and whether or not the associated Jacobian Matrix _ITSELF_ is *singular* (i.e. possesses a Matrix Inverse) are two TOTALLY DIFFERENT *versions* of the meaning of *singular.*
In many videos, the circumstance of *Robot Arm singularity* is simply defined as the moment when the Jacobian Matrix exhibits a ZERO VALUE for the calculation of its associated Determinant. Since only *square matrices* can even HAVE a Determinant, *^this^ choice* for defining the condition of *Robot Arm singularity* (which is the "habit" of many _other_ videos on this topic) would seem to be a deficient choice.
Your choice, for defining the condition of *Robot Arm singularity,* by defining it as the *group of Robot Arm JOINT ANGLES* that causes a value of Jacobian Matrix *rank* to occur THAT IS *less than* the *MAXIMUM rank* possible (exhibited at _some_ particular grouping of Robot Arm JOINT ANGLES) would seem to be a *far superior Definition* for the *mathematical* onset of the circumstance of *Robot Arm singularity.*
The book also mentions the singularities occur when the Jacobian matrix's rank drops from its maximal rank which is the general case. When the Jacobian matrix is square (i.e. a special case), the shortcut is to check its determinant. I prefer to go with the rank's notion.
This reminds me of school, I'd just sit and look at the teacher. With absolutely no idea what they are talking about, or even why they are talking at all. At least I know why this guy is talking 😐.
NICE SHIRT!
1:50 THICC
you made my laugh so hard