Precision forward design for 3D printing using kinematic sensitivity via Jacobian matrix considering uncertainty

Abstract

This paper presents a precision forward design method for 3D printing (3DP) using kinematic sensitivity via Jacobian matrix (KSJM) considering uncertainty. The advanced manufacturing such as 3DP profoundly affects us everywhere. However, in many cases, practical uncertain factors such as mechanical and thermal effects affect the precision unquantifiably. Aiming at realizing forward design from requirements to performance, the various kinematic chains are summarized to propose the concept of kinematic sensitivity. The Jacobian matrix which reflects the relationship between input error and output error is decomposed through singular value decomposition (SVD). The KSJM is hereby proposed by furtherly defining four sensitivity parameters: compositive amplification factor of error, reliability of error, absolute amplification factor of error, and comprehensive index of error. The influence of uncertainty such as thermal deformation on the accuracy of end-effector in Cartesian space is investigated by heat fluid-solid coupling simulation and piecewise fitting of thermal deformation. Taking delta 3DP robot as example, the kinematic chains and error sensitivity of the multi-body system are addressed. The physical experiment is implemented via attitude sensors with accelerometers, gyroscopes, and magnetometer. The results proved that trajectory accuracy and reliability can be improved especially under complex random uncertainty.