Papers to read for the 9th Feb 2017
Degrees of freedom
- Serial chains
- e.g. most extremities (arms/legs)
- Parallel chains
- e.g. rib cage
- Steward platform
Grueblers equation and Kutzbach criterion
Relates degrees of freedom to the links and joints.
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 ||DoF||type |
| Revolute || 1||R |
| Prismatic || 1||P |
| Screw || 1||R+P |
| Cylindrical || 2||RT |
| spherical/Ball|| 3||RRR |
| Planar || 3||RRT |
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
- a revolute joint
- a prismatic joint?
Robot reachable workspace
Robot (and human) workspace is limited by
- Joint range of movement
- boundary singularities (can't move beyond the workspace boundary)
- internal singuularities (joint axes come into alignment)
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
- concept of affordance in robotics is championed by Ralph Pfeifer (Zurich University), that the morphology is exploited by the central nervous system
- Foldable robots (see papers for review)
- Flexible (snake/octopus/salamander robots) e.g. Auke Jan Ijspeert EPFL
- Climbing/Jumping/Cockroach/Gecko robots (e.g. Robert J Full Berkeley)
- morphology for specific applications, any number of robot grippers are designed for the task (eg industrial assembly and packing, agriculture). Compare these with the capabilities of the human hand.