Papers to read for the 9th Feb 2017

A Robot Teaches Itself How to Walk from swissnex San Francisco

Cognitive Robotics and Artificial Intelligence from swissnex San Francisco

Degrees of freedom

Grueblers equation and Kutzbach criterion

Relates degrees of freedom to the links and joints.


$m=3(n-j-1)+\sum^j f_i$


$m=6(n-j-1)+\sum^j f_i$

where $n$=number of links, $j$= number of joints, $f_i$ = d.o.f. in joint $i$, $m$=degrees of freedom Usually need to have at least one actuator per degree of freedom

The lower pairs

Six lower order kinematic pairs

name DoFtype
Revolute 1R
Prismatic 1P
Screw 1R+P
Cylindrical 2RT
spherical/Ball 3RRR
Planar 3RRT

In fact the screw is the most general robot joint. All rigid motion of links in a robot can be described as a combination of screw motions.

Question, how does a screw joint represent

Anatomical joints

Robot reachable workspace

Robot (and human) workspace is limited by

Singularities are where the Jacobian is singular, (in this case the Jacobian is a location dependent relationship beween the joint veolcity and the endpoint velocity) \[ \Delta x=J \Delta\theta \]

So if J is singular, then to achieve a specific $\Delta x$ requires an infinite joint velocity vector.

Likewise \[ \tau=J^T F \] where $\tau$ is the joint torque and $F$ is the end point force so at a workspace singularity there is no ability of the joints to opose the external force

Affordance and morphology