Please enable JavaScript.
Coggle requires JavaScript to display documents.
Kinematics of Serial Robot ofPosition Analysis - Coggle Diagram
Kinematics of Serial Robot ofPosition Analysis
Representation of a Frame
Homogeneous Transformation
F is a 4x4 matrix.
Top-left 3x3 is the Rotation Matrix.
Top-right 3x1 is the Position Vector (p).
Frame Constraints
Vectors must have Unit Length and be Mutually Orthogonal.
Must satisfy the Right-Hand Rule (n x o = a).
Frame Componrnts
Directional Unit Vectors (n, o, a).
Position Vector (p).
Frames
Represents position and orientation of an object/link.
Defined relative to a fixed Reference Frame
Representation of Transformations
Pure Transformation
Movement along axes (dx, dy, dz) without any change in orientation.
Trans(dx, dy, dz) matrix form.
General Purpose
Matrix operation to change the location of a frame or point.
p_new = T * p_old.
Pure Rotation
Change in orientation about an axis without any change in position.
Rot(x, θ), Rot(y, θ), Rot(z, θ) matrices.
Representation of Combined Transformations
Final HTM Expression (T_final)
Matrices are multiplied in the reverse order of the physical sequence.
T_final = T_n
...
T_2 * T_1.
Successive Operations
Sequence of Rotations and Translations.
Applied relative to the fixed reference frame.
Matrix Multiplication Rule
The operation is non-commutative (T1
T2 ≠ T2
T1).
Order of multiplication is crucial.
Primary Kinematic Application
Used for Forward Kinematics.