Performance Analysis Of A Kind Of Foldable Parallel Mechanisms

The main content of this article is studying how to use foldable branches to buildparallel mechanisms, in order to reduce the height, the space occupied area and the volumeof the parallel mechanism. It can expand the application of parallel mechanisms wherespace is small. The workspace, stiffness, singularity of the foldable parallel mechanism areanalyzed to evaluate the effect of the attachment of the foldable and parallel mechanism.Firstly, the category of the foldable branches, which is suitable to constitute parallelmechanism, is analyzed. The foldable parallel mechanism is divided into three kinds,which is Single-Foldable branch, Double-Foldable branch and Multi-Foldable branch.Based on the screw theory and parallel mechanism theory, the kinematic model and theequalization to normal Series single branch are deduced. The kinematic model of thebranches those with multi-links, multi-chains and multi-cross is built.Secondly, the6-DOF foldable parallel mechanism is designed and optimization byseeking the optimal structure parameters. In order to increase the workspace height, theSLEs are used to replace the traditional Double-Foldable branch, and build theMulti-Foldable branch. Build the kinematic model of the mechanism with closed-looplinear drive.Thirdly, the workspace of the6-DOF parallel mechanism is calculated to evaluate theeffect to the workspace in vertical direction. After that, the directional stiffness of the6-DOF parallel mechanism is deduced. The rotational and directional stiffness in xy and zdirection when the moving platform is lifting are illustrated as faces and lines. The methodto find all the singularity of the mechanism is analyzed, and the relationship between thedirectional stiffness and the singularity is analyzed. The changement of the translationalstiffness and rotational stiffness when the mechanism get close to singularity is analyzed.Finally, a method to build the kinematic of lower-mobility parallel mechanism ismentioned based on the matrix QR decomposition. The forward and inverse kinematicmodel is built based on the first and second order influence matrix. The velocity andacceleration constraint matrix are also built. Based on the principle of virtual work, the flexibility matrix and directional stiffness are built. The coupling kinematic of the3RPSmechanism is analyzed. The directional stiffness of3RPS is analyzed to verify thestructural constraint, and the directional infinity stiffness is visually describes by thedistribution of spherical coordinates. At last, the influence of the redundant branchstiffness of3RRS+RUS to the mechanism is analyzed by calculating the directionalstiffness.