Lateral bending models of spring spine for cable-driven parallel mechanism

Cable-driven parallel robots with flexible spring spine were present to mimic a human neck. The fixed base and moving platform of the robots are connected by cables and a compression spring. The spring serves as cervical spine to support and facilitate the motion of moving platform corresponding to human head. The cables serve as the muscles around human neck to drive the robot. The bending motion of the compression spring spine is the key to inverse kinematics of the robots. In this paper, we compare two types of lateral bending models of the compression spring. The first one takes lateral bending of the spring as a circular arc; therefore, homogeneous transformation matrix of the robot can be calculated based on geometry, which leads to solving inverse kinematics directly. The second one takes lateral bending of the spring as a linear two-order differential equation; therefore, inverse kinematics has be combined with the statics analysis for possible solutions. Inverse kinematics of the robots were solved and simulated with the two types of bending equations. The simulation results show that the two have similar cable length for given posture of the moving platform. However, the circular arc case can guarantee the nonnegative cable force constraint only with small bending angles of the moving platform.