Please enable JavaScript.
Coggle requires JavaScript to display documents.
Kinematics of Serial Robots - Coggle Diagram
Kinematics of Serial Robots
Matrix Representation
Representation of point in Space
Eg: P= axi + byj + czk
Representation of a vector in space
Eg: Pab = (bx - ax)i + (by - ay)j + (bz - az)k
Where the vector starts at "a" and ends at "b".
Representation of a Frame at the Origin of a Fixed-Reference Frame
In this, we use x,y,z axes as a fixed reference frame (Fx,y,z) and a set of axes n,o,a(normal, orientation, approach) to represent another frame relative to the fixed reference frame.
Representation of a Frame relative to a fixed Reference Frame
In this the Frame is not at the origin, but it is relative to the fixed reference frame(origin) and is described by a vector between the origin of the frame and the origin of the reference frame
Representation of a Rigid body
In this the object is permanently attached to the frame and the orientation and position relative to the frame are always known provided the frame can be defined in space.
Homogeneous Transformation Matrices
The word Homogeneous means same. and in the case of matrices, it means same rows and columns(eg,3x3,4x4). because it will be easy to multiply square matrices than rectangular matrices.
In the case of Equations of motions of the robotics, we need to have matrices of same rows and columns.
If we represent the orientation and position in the same matrix.
1.We can add the scale factor that will make 4x4.
2.we can drop the scale factor that will make 3x3.
3.we can drop scale factor and add 4th column with zeros for keeping the square matrix.
and matrices of this kind are known as Homogeneous matrices.
Representations of Transformations.
A transformation represents the movement of a frame, vector, or object in space relative to a fixed reference frame.
The Transformations may be one of the following:
3.Representation of combined transformations: It involves the successive translations and rotations about a fixed reference frame or the moving current frame axes.
4.Transformations relative to current(moving) Frame: This means that rotation may be made relative to the n-axis of the current(moving)frame and not in the x-axis of the reference frame(global frame).
5.Mixed Transformations Relative to Rotating and Reference Frames: it involves a combine motion relative to both the fixed reference frame and the rotating (moving) frame.
1.Representation of pure Translation:
A pure translation occurs when a frame moves in space without changing its orientation.
Here, the unit vectors stay the same, and only the origin shifts relative to the reference frame.
2.Representation of a pure Rotation about an axis:
A pure rotation about an axis means the frame(fnoa) rotates around a fixed axis(fxyz) while its origin remains in the same place.
The orientation of the frame changes according to the rotation matrix, but its position does not shift.
Inverse of Transformation Matrices
The inverse of a transformation matrix reverses a movement, bringing the frame back to its original position and orientation.
It is obtained by transposing the rotation part and applying the negative of the translated vector adjusted by that rotation.
Forward and Inverse Kinematics of Robots
Forward Kinematics
All the joint variables are known; we have to find the position and orientation of hand of the robot.
Inverse Kinematics
It involves calculating each link length and joint angle, so that the hand will be at the desired position and orientation.