Table of Contents
Understanding how to derive velocity and acceleration in robotic arms is essential for precise control and movement planning. This article provides a clear, step-by-step approach to calculating these parameters based on joint angles and link parameters.
Kinematic Foundations
The process begins with the kinematic equations that relate joint parameters to the position of the end effector. Forward kinematics determines the position and orientation based on joint angles.
Velocity and acceleration are then derived by differentiating these equations with respect to time. This involves calculating the Jacobian matrix, which links joint velocities to end-effector velocities.
Calculating Velocity
Joint velocities are typically known or measured. To find the end-effector velocity, multiply the Jacobian matrix by the vector of joint velocities:
End-effector velocity = Jacobian × Joint velocities
Calculating Acceleration
Acceleration involves both joint accelerations and the rate of change of the Jacobian. The end-effector acceleration is calculated as:
End-effector acceleration = Jacobian × Joint accelerations + Jacobian derivative × Joint velocities
Practical Steps
- Determine joint angles and velocities at the current time.
- Calculate the Jacobian matrix based on the current joint configuration.
- Multiply the Jacobian by joint velocities to find end-effector velocity.
- Compute the Jacobian derivative if joint accelerations are known.
- Combine these to find the end-effector acceleration.