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Solution to Inverse
Kinematics
Hitesh Mohapatra
https://www.linkedin.com/in/hiteshmohapatra/
What is Inverse Kinematics ?
• In Robotics, Inverse Kinematics makes use of the
Kinematics equation to determine the joint
parameters that provide a desired position for
each of the robots and effectors.
• Inverse Kinematics transforms the motion plan
into joint actuator trajectories for the robot.
Now, imagine if you would like the
end effector of an Articulated body
to reach a particular target position.
This means that you know the end
effector position you would like to
target, but you don’t know what the
pose of the articulated body needs
to be for the end effector to reach
the target position.
Uses of Inverse kinematics
 Used for a Humanoid Arm to reach for an object.
 Can also be used for Foot Stepping.
 Used as an Animation tool.
 Used to predict direction.
How to solve Inverse kinematics problem ?
• We are Provided with the desired position of the robot’s hand and
we need to find the angles at all the robot’s joints.
•
• Xhand = lcosØ
(forward position
solution)
cosØ = Xhand/l
Ø = cos-1(Xhand/l)
Example:
Given: Xhand, Yhand,
Øhand
Find: Ø1, Ø2 and Ø3
B: length of imaginary
line
q1: angle between X-axis
and imaginary line
q2: interior angle
between imaginary line
and link l1
Solution:
B2 = Xhand2 + Yhand2 (by the Pythagorean theorem)
q1 = ATan2(Yhand/Xhand)
q2 = acos[(l12 - l22 + B2)/2l1B] (by the law of cosines)
Ø1 = q1 + q2 (I know you can handle
addition)
Ø2 = acos[(l12 + l22 - B2)/2l1l2] (by the law of cosines)
Ø3 = Øhand - Ø1 - Ø2
Let’s take an example:
THANK YOU

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Solution to Inverse Kinematics

  • 1. Solution to Inverse Kinematics Hitesh Mohapatra https://www.linkedin.com/in/hiteshmohapatra/
  • 2. What is Inverse Kinematics ? • In Robotics, Inverse Kinematics makes use of the Kinematics equation to determine the joint parameters that provide a desired position for each of the robots and effectors. • Inverse Kinematics transforms the motion plan into joint actuator trajectories for the robot.
  • 3. Now, imagine if you would like the end effector of an Articulated body to reach a particular target position. This means that you know the end effector position you would like to target, but you don’t know what the pose of the articulated body needs to be for the end effector to reach the target position.
  • 4. Uses of Inverse kinematics  Used for a Humanoid Arm to reach for an object.  Can also be used for Foot Stepping.  Used as an Animation tool.  Used to predict direction.
  • 5. How to solve Inverse kinematics problem ? • We are Provided with the desired position of the robot’s hand and we need to find the angles at all the robot’s joints. • • Xhand = lcosØ (forward position solution) cosØ = Xhand/l Ø = cos-1(Xhand/l)
  • 6. Example: Given: Xhand, Yhand, Øhand Find: Ø1, Ø2 and Ø3 B: length of imaginary line q1: angle between X-axis and imaginary line q2: interior angle between imaginary line and link l1
  • 7. Solution: B2 = Xhand2 + Yhand2 (by the Pythagorean theorem) q1 = ATan2(Yhand/Xhand) q2 = acos[(l12 - l22 + B2)/2l1B] (by the law of cosines) Ø1 = q1 + q2 (I know you can handle addition) Ø2 = acos[(l12 + l22 - B2)/2l1l2] (by the law of cosines) Ø3 = Øhand - Ø1 - Ø2
  • 8. Let’s take an example:
  • 9.