Dynamic and Compliant Characteristics of a Cartesian-Guided Tripod Machine

This paper is focused on the dynamic and compliant characteristics of a three-axis parallel kinematic machine called a Cartesian-guided tripod (CGT), which has a passive leg locking the platform three rotational degrees of freedom. Because no constraint mechanism is perfect with infinite rigidity, a compliance model has been developed to determine the maximum amplitude of the passive-leg parasitic motions using given loads. System compliance, dynamic characteristics, vibration modes, and servo-contouring errors of the CGT driving system have also been evaluated under high-speed machining conditions. The nonlinear dynamic effects, such as inertia and gravity, can be controlled within acceptable accuracy using the high-gain servo-feedback control techniques. The CGT dominant flexible mode occurs on the horizontal platform-leg vibration. The platform-leg flexible mode can produce significant jerk-induced mechanical vibration on the platform when a sudden velocity change is commanded. Look-ahead Cartesian-based path acceleration and deceleration control was found to be an efficient tool to reduce the jerk-induced mechanical vibration, although the CGT was drive controlled at the joint level. It was found that at high acceleration application, such as high-speed mold and die machining, the elastic elongation of the driving leg caused by the high acceleration force became the dominant contouring error sources.