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KINEMATIC RELATIONSHIP BETWEEN
ADJACENT LINKS
Hitesh Mohapatra
https://www.linkedin.com/in/hiteshmohapatra/
KINEMATICS
KINEMATICS – the analytical study of the geometry
of motion of a mechanism:
• with respect to a fixed reference co-ordinate
system,
• without regard to the forces or moments that
cause the motion.
In order to control and programme a robot we must
have knowledge of both its spatial arrangement and a
means of reference to the environment.
OPEN CHAIN MANIPULATOR KINEMATICS
Mechanics of a manipulator can be
represented as a kinematic chain
of rigid bodies (links) connected by
revolute or prismatic joints.
One end of the chain is constrained
to a base, while an end effector is
mounted to the other end of the
chain.
The resulting motion is obtained by
composition of the elementary
motions of each link with respect to
the previous one.
CLOSED KINEMATIC CHAIN
Much more difficult.
Even analysis has to take into account statics,
constraints from other links, etc.
Synthesis of closed kinematic mechanisms is very
difficult.
MAPPING OF FRAMES
● MAPPING – Changing the description of a point in
space from one frame to another.
● MAPPING BETWEEN ROTATED FRAMES
● MAPPING BETWEEN TRANSLATED FRAMES
● COMPOSITE MAPPING
ROTATED FRAMES
TRANSLATED FRAMES
COMPOSITE MAPPING
COMPOSITE TRANSFORMATION
COORDINATE FRAMES
DIRECT KINEMATICS
One joint: xi = Axi−1.
Chain of joints: xn−1 = An−1 An−2 . . . A1
A0 x0. Easy to compute (matrix multiplication).
Unique solution.
THANK YOU

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Kinematic Relationship Between Adjacent Links

  • 1. KINEMATIC RELATIONSHIP BETWEEN ADJACENT LINKS Hitesh Mohapatra https://www.linkedin.com/in/hiteshmohapatra/
  • 2. KINEMATICS KINEMATICS – the analytical study of the geometry of motion of a mechanism: • with respect to a fixed reference co-ordinate system, • without regard to the forces or moments that cause the motion. In order to control and programme a robot we must have knowledge of both its spatial arrangement and a means of reference to the environment.
  • 3. OPEN CHAIN MANIPULATOR KINEMATICS Mechanics of a manipulator can be represented as a kinematic chain of rigid bodies (links) connected by revolute or prismatic joints. One end of the chain is constrained to a base, while an end effector is mounted to the other end of the chain. The resulting motion is obtained by composition of the elementary motions of each link with respect to the previous one.
  • 4. CLOSED KINEMATIC CHAIN Much more difficult. Even analysis has to take into account statics, constraints from other links, etc. Synthesis of closed kinematic mechanisms is very difficult.
  • 5. MAPPING OF FRAMES ● MAPPING – Changing the description of a point in space from one frame to another. ● MAPPING BETWEEN ROTATED FRAMES ● MAPPING BETWEEN TRANSLATED FRAMES ● COMPOSITE MAPPING
  • 11. DIRECT KINEMATICS One joint: xi = Axi−1. Chain of joints: xn−1 = An−1 An−2 . . . A1 A0 x0. Easy to compute (matrix multiplication). Unique solution.