Inertial analyses based on the generalized inertia matrix for parallel robots

Analyzing the inertial properties is meaningful for parallel robots, especially those interacting with the environment. This paper provides tools for the analysis of the inertial properties of parallel robots based on the generalized inertia matrix (GIM). Since most interactions between the environment and robots happen through the mobile platform, the inertia of the whole robot reflected at the platform is considered. In this framework, the GIM is expressed in Cartesian space to yield inertial characteristics with a clear physical meaning. Then, the inertia of the whole robot is thereby reduced to an equivalent mass/inertia at the platform. Unlike for serial robots, obtaining the GIM of parallel robots in Cartesian space is complex due to the inherent closed-loop structures and the possibility of including two different types of redundancy. Two methods are proposed to solve the mentioned problems, which can simplify the derivations of the required GIMs for parallel robots. Detailed analysis and usages of the proposed methods are given based on different examples, and the results demonstrate the effectiveness of the proposed approaches.