kinematics of robots
DESCRIPTION
Apuntes cinemática de robotsTRANSCRIPT
Kinematics of robotsM. C. Martín Montes Rivera
Kinematics
Kinematics applied to robots it is the science that studies movement of a robot without
considering forces
There are 2 kinds of kinematical problems in robots, first is known as forward kinematics and
second inverse kinematics.
Forward kinematics it is to get the position and orientation of end effector with joint
coordinates.
Inverse Kinematics allows to get the required joint coordinates to reach a desired
position and orientation
Forward Kinematics
To find a position or orientation of an end effector robot, requires of a
homogeneous matrix, which have this information.
With this homogeneous matrix it is possible to get equations depending of
joint coordiantes.
Example with a few DOF
Robots with more DOF
Methodology using transformation matrixes which are simpler to understand
and program in a computer.
In general industrial robots have n degrees of freedom, n joints and n links,
which means that every link-joint it’s a DOF.
Transformation matrix that changes two consecutive coordinate system it is
represented by (last one to actual).
Examples
Exercise
Obtain the equations that represents position of end effector robot
Denavit-Hartenberg Algorithm
Denavit-Hartenberg (D-H) AlgorithmFollowing directions according to its joints, revolute axis
point out of the rotation and prismatic in the same
direction.
X axis must be selected pointing to end effector
Example
Exercise D-H and Kinematic equations
Exercise D-H and kinematic equations
Exercise D-H and kinematic equations
Exercise D-H and kinematic equations
Exercise D-H and kinematic equations
Exercise D-H and kinematic
equations
Orientation Angles
Orientation
Considering that a vector with magnitude k and components given by
If there is a rotation around angle theta in OZ axis, it is required to perform
the bellow operations in order to make concurrency of k with OZL, and then
get the rotation angle.
And with the next equivalences
After perform operations and considering that
Homogeneous matrix obtained is:
Then all components are equaled to
Orientation
Considering every angle between 0º and 180º and equations 3.74 and 3.75 can
be obtained
With alpha for x angle, beta
for y angle and theta for zeta
angle.
References
Fundamentos de Robótica: Antonio Barrientos, Luis Felipe Peñín, Carlos Balaguer, Rafael Aracil
Robot Dynamics and Control: Mark W. Spong, Seth Hutchinson, and M. Vidyasagar