rotation matrix

Among four joints of human foot in the ankle area, the tibiotalar and subtalar joints play the most important role in making it possible for the foot to perform rotational movements such that kinematic behavior of foot is almost completely affected by orientation of their rotation axes. Deviation of the axis of rotation from the normal position can impair the function of the ankle and even the lower extremity. In this study, a new non-invasive method has been proposed, through which, using a gyroscopic mechanism, the orientation of the rotation axes of the tibiotalar and subtalar joints can be determined. This method is based on indirect data acquisition from the kinematic behavior of the foot. Using the calculated matrices and through the optimization method, the orientation and position of the rotation axes were respectively calculated at relatively high precision. These results were also assessed in practice by building an ankle mechanical model and a robotic gyroscopic mechanism which is used as a robotic rehabilitation device for ankle rehabilitation. Obtained results show that the maximum error in determining the orientation of the rotation axes is about 2 degrees.

Parallel mechanisms are more utilized, because of their extra precision and stiffness in comparison with serial mechanisms. Measuring position and orientation (pose) of parallel robot end effector and performing kinematic calibration, is a guaranty for, moving precision of these robots. Through different measurement devices, machine vision has advantages such as low cost, simplicity in use and rather appropriate precision. In this research, in order to measure pose of end effector of a 4-DOF (degree of freedom) parallel robot, a vision-based measurement system, is designed and implemented in Matlab software. The laboratory device is a stereo camera. Camera calibration is carried out in Matlab. A triangular shape is used as feature on the robot end effector. By processing the images acquired from pose of end effector, in designed measurement system, rotation matrix and translation vector are obtained and the exact position of the end effector is revealed. For investigating precision and accuracy of proposed measurement system, a conventional measurement method with the help of gauge block and indicator, is used. According to the nature of machine vision, the results achieved in this examination, are acceptable; although better precision can be attained by improving devices used in this research.