Pre-tightening Force Analysis of a Pre-stressed Six-axis Force Sensor

By using sphere pair with unilateral constraint, the limbs of the proposed pre-stressed six-axis sensor must be under pressure in the measurement process, so prior to measurement, a certain preload must be applied to the sensor. The viable limbs' number of the pre-stressed six-axis force senor is determined by using convex theorem. By solving the static equilibrium equation of sensor, the reacting forces on limbs are divided into two parts: the particular solution is generated by the external force, while the homogeneous solution is only concerned with the pre-tightening force. The number of parameters to be determined in homogeneous solution is decreased by linear transform, and the method for determining the pretightening force is derived to make all the limbs compressed when it is subjected to the expected range of external force. A numerical example to determine the pre-tightening force of the force sensor is performed. The numerical example results show that the force on limbs can always maintain positive value with the appropriate pre-tightening force, which proves the correctness of the theoretical analysis and the validity of the sensor structure.