Robotics class notes.
Class night!
I'm taking CS 223A from Stanford Engineering everywhere, and i'm making my notes on class here. I'm watching class 2 tonight, here's part 1 of my notes
All joints can be reduced to two different types:
revolute - Twisting around one axis
prismatic - extending/contracting along one axis
Each joint offers 1 degree of freedom.
All varitions on joints can be reduced to a combination of these two types of joints:
Sphereical joint is just a combination of three revolute joints, providing 3 degrees of freedom.
Generalize coordinates:
For any rigid body, 6 coordinates are needed to describe it's position in space:x,y,z, rot z, rot y, rot x
Without the joints, a system of rigid bodies can be described using 6n parameters, where n is the number of rigid bodies which make up the system.
if there are n parts we need 6n parameters to describe bodies, 5n parameters to describe the position of it's joints, the overall system has 6n - 5n = n degrees of freedom.
Operational coordinates = task coordinates
End effector configuration parameters d= a set of parameters (x1, x2, x3, x4, ... ) which completely specifies the position and orientation of the end effector of a system.
Terms to look up:
Direction cosines?
Rotation matrix
6 degrees of freedom is suffucient in 3 dimensions to place the end effector anywhere in the space
3 degrees of freedom is sufficient in 2 dimensions ( planar robot ) to place the end effector anywhere in the plane.
1 degree of freedom is suffucient in 1 dimension (linear? robot) to place the end effector anywhere in the plane.
joint coordinates map to joint space. Movement planning takes place in Joint space.
c-obstacles are plotted in the joint space for movement planning.
Operational coordinates map to operational space.
redundancy refers to adding extra joints such that the degrees of freedom of the robot exceeds the number of degrees of freedom necessary for the operational space.
degree of redundancy is the number of degrees of freedom by which it exceeds the dimensions requirements.
Forward kinematics will be covered next week.
How can we describe the position of a point in space?
point p is positioned relative to a reference point -
Coordinate frames:
revolute joints rotate the coordinate frames about the origin.
prismatic joints translate the coordinate frames along an axis.
How do we describe the coordinate frame (B) in relation to the absolute frame (A)?
Position P is a vector (aXb,aYb,aZb)
Rotation R is a rotation matrix
R = r1,1r1,2r1,3
r2,1r2,2r2,3
r3,1r3,2r3,3
I've forgotten way too much stuff about Matrix mathematics.
Breaking now for Heroes. Back in an hour.
I'm taking CS 223A from Stanford Engineering everywhere, and i'm making my notes on class here. I'm watching class 2 tonight, here's part 1 of my notes
All joints can be reduced to two different types:
revolute - Twisting around one axis
prismatic - extending/contracting along one axis
Each joint offers 1 degree of freedom.
All varitions on joints can be reduced to a combination of these two types of joints:
Sphereical joint is just a combination of three revolute joints, providing 3 degrees of freedom.
Generalize coordinates:
For any rigid body, 6 coordinates are needed to describe it's position in space:x,y,z, rot z, rot y, rot x
Without the joints, a system of rigid bodies can be described using 6n parameters, where n is the number of rigid bodies which make up the system.
if there are n parts we need 6n parameters to describe bodies, 5n parameters to describe the position of it's joints, the overall system has 6n - 5n = n degrees of freedom.
Operational coordinates = task coordinates
End effector configuration parameters d= a set of parameters (x1, x2, x3, x4, ... ) which completely specifies the position and orientation of the end effector of a system.
Terms to look up:
Direction cosines?
Rotation matrix
6 degrees of freedom is suffucient in 3 dimensions to place the end effector anywhere in the space
3 degrees of freedom is sufficient in 2 dimensions ( planar robot ) to place the end effector anywhere in the plane.
1 degree of freedom is suffucient in 1 dimension (linear? robot) to place the end effector anywhere in the plane.
joint coordinates map to joint space. Movement planning takes place in Joint space.
c-obstacles are plotted in the joint space for movement planning.
Operational coordinates map to operational space.
redundancy refers to adding extra joints such that the degrees of freedom of the robot exceeds the number of degrees of freedom necessary for the operational space.
degree of redundancy is the number of degrees of freedom by which it exceeds the dimensions requirements.
Forward kinematics will be covered next week.
How can we describe the position of a point in space?
point p is positioned relative to a reference point -
Coordinate frames:
revolute joints rotate the coordinate frames about the origin.
prismatic joints translate the coordinate frames along an axis.
How do we describe the coordinate frame (B) in relation to the absolute frame (A)?
Position P is a vector (aXb,aYb,aZb)
Rotation R is a rotation matrix
R = r1,1r1,2r1,3
r2,1r2,2r2,3
r3,1r3,2r3,3
I've forgotten way too much stuff about Matrix mathematics.
Breaking now for Heroes. Back in an hour.