# Wearable Intertace for Teleoperation of Robot Arms - WITRA

# Direct Kinematics

A key factor in this project is the kinematics of the human arm. We use it in order to convert the angles measured by the IMUs to the position of the user's wrist. This position is mapped to the robot's working space and used as reference of position for the robots end-effector. In this manner, WITRA is applicable to any kind of robot (cartesian, cylindrical, spherical, SCARA, antropomorphic) for which we can calculate its inverse kinematics.

We deal with a simplified geometry, that is, considering only the main 7 degrees of freedom (DoF) and ignoring the movement of the scapula and forearm pronation. Thus, the DoFs considered are: 3 for the shoulder, which acts as a spherical joint; 1 for the elbow; and 3 for the wrist, also a spherical joint.

Therefore, in this text we calculate the direct kinematics of the human arm. Our goal is to, given the rotations of each joint of the human arm, calculate a trasnformation matrix that contains information about the position of the wrist in cartesian coordinates, as well as the spacial orientation of the hand. The transformation matrix we want to develop has the form of

Each rotation (DoF) at the human arm is represented by a 4x4 matrix Ai, with i = 1, ..., 7. Furthermore, our reference frame (x0,y0,z0) is placed at the shoulder. Hence, the 7 matrices are

The resulting matrix is given by

This matrix, Awrist has the same strucutre of the transformation matrix shown in (1), where

Therefore, it is possible to calculate the position of the human’s wrist in terms of cartesian coordinates, given the rotation in each joint. The rotation of each joint can be measured using inertial sensors (IMUs).

# References

[1] N. I. Badler, D. Tolani. Real-Time Inverse Kinematics of the Human Arm. Unversity of Pennsylvania Scholarly Commons, 1999.

[2] J. J. Craig. Introduction to Robotics - Mechanics and Control. Pearson Prentice Hall, 2005.

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