Relates degrees of freedom to the links and joints.
Planar
$m=3(n-j-1)+\sum^j f_i$
Spatial
$m=6(n-j-1)+\sum^j f_i$
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
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?
Anatomical joints
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 Rolf Pfeifer (Zurich University), that the morphology is exploited by the central nervous system
Examples
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.