Kinematics of medical robots Flashcards
What are kinematics?
The study of movement
The branch of classical mechanics that describes the motion of objects without consideration of the forces that cause it
DOF of motion
DOF of sensing
DOF of actuation
The DOF of a mechanism does not always correspond to number of joints
Why do we need kinamatics?
Determine endpoint position and/or joint positions
- Calculate mechanism velocities, accelerations, etc.
- Calculate force-torque relationships
what are degrees of freedom?
Number of independent position variables needed to in order to locate all
parts of a mechanism
*DOF of motion
*DOF of sensing
*DOF of actuation
The DOF of a mechanism
does not always correspond to number of joints
how many DOF does a four bar linkage usually have and whats the relationship between input and output link angle be computed?
Commonly used 1-DOF mechanism
relationship can be computed from geometry
What are the different types of joints and which is the most common for medical robots?
Revolute - most common for robots - one DOF - 2 plate one pin through both sliding around pin one plate on top of other
Prismatic - 1 DOF - only slides up and down
Cylindrical - 2 DOF - One rotation and one vertical translation up and down
Planar - 2 DOF
Screw - 1 DOF - circle screws around cylinder screw
Spherical - ball and socket - 3 DOF
note
- think of a mechanism/manipulator/interface as a set of bodies connected by a chain of joints
What are the two types of coordinate sets in terms of kinematics?
Joint space
Cartesian space
can move between joint space and cartesian space
What is forward kinematics?
based on joint angles, calculate end-effector position
if you know q1 and q2 of the generalized joint variables, this can be used to calculate the cartesian coordinate x,y and z
inverse kinematics is the opposite so from cartesian coordinate system to joint angles/joint variables
What type of forward kinematics is usually used for robots?
Relative forward kinamatics
what is inverse kinematics, whats it used to calculate, and what its not used for?
Using the end-effector position, calculate the joint angles necessary to achieve that position
Not used often for input devices or for robot control
But useful for planning
There can be:
* No solution (workspace issue)
* One solution
* More than one solution
What are the two methods to calculate inverse kinematics?
Algebraic method (using transformation matrices)
Geometric method
What is the Jacobian and what does it do?
A matrix transformation that turns one quantity into another
can be used to calculate the end-effector velocity
What is a singularity in terms of the Jacobian?
Many devices will have configurations at which the
Jacobian is singular
This means that the device has lost one or more degrees of freedom in Cartesian Space
Two kinds:
* Workspace boundary
* Workspace interior
When is a Jacobian non singular?
When the matrix is invertible
how do you check the invertibility of j?
taking the determinant of J
if the determinant is equal to 0, the J is singular
can use this method to check which values of theta will cause singularities
What can the Jacobian be used to relate?
can be used to relate joint torques to end effector forces
t = J^TF
