Research On Lower Mobility Parallel Mechanisms Based On Parallelograms With Variable Length

Parallel mechanisms have been widely used in the industry due to the advantages of good rigidity,low inertia and high positional accuracy.In particular,the lower mobility parallel mechanisms have the significant characteristics of fewer components,compact structure and simple control in comparison with six-degree-of-freedom parallel mechanisms.Moreover,parallel mechanisms with the motors mounted on or close to the base can take the lightweight rod as the moving arm,which allows the end effector to obtain extremely high speed and acceleration.Therefore,lower mobility parallel mechanisms with the above-mentioned characteristics are suitable for picking and placing objects at high speed on the production line.Through the analysis of the lower mobility parallel mechanisms suitable for the above occasions,it can be found that the core design idea is that parallelograms are applied as the closed-loop sub-limbs,which can ensure that the end-effector always moves in translation with respect to the base.Therefore,based on the research on the parallelogram closed-loop sub-chains,a series of kinematic limbs based on parallelogram with variable length are proposed,which include synchronous telescopic parallelogram closed-loop sub-chain and compound kinematic limb.Controlled by one motor,the synchronous telescoping of a set of opposite sides in the parallelogram can be achieved to ensure that the other set of opposite sides always keeps parallel.The parallelogram with variable length not only has the special parallel geometric relationship in the parallelogram closed-loop sub-chain,but also extends the application range of the parallelogram closed-loop sub-chain.According to the configuration derivation,a family of lower mobility parallel mechanisms are obtained by the utilization of the above-mentioned kinematic limbs,such as: novel two-translation parallel mechanism,novel three-translation parallel mechanism,and novel three-translation and one-rotation parallel mechanism.Compared with the existing Diamond mechanism,Delta mechanism,X4 mechanism and other similar mechanisms,all new lower mobility parallel mechanisms have the advantages of compact structure,small footprint and simple manufacturing.Since higher-order kinematics can easily solve the simplification and calculation of closed-loop equations,the degrees of freedom of the above-mentioned lower mobility parallel mechanisms with closed-loop sub-chains are obtained by introducing high-order kinematics,that is,closed-loop speed equation based on screw theory,which verifies the correctness of the derivation of the lower mobility parallel mechanisms.Moreover,by the simplified kinematics model of the new lower mobility parallel mechanisms,the position,velocity,acceleration and singularity are analyzed,and the reachable working space are calculated.According to the rigid body model of the novel two-translation parallel mechanism,the mathematical model of the speed and acceleration of each limb is established,and the Jacobian matrix of each limb is obtained.Based on the virtual work principle method,an overall inverse dynamic model of the mechanism is established combined with the results of the kinematic analysis of the novel two-translation parallel mechanism.Through the numerical simulation of MATLAB software,the driving force or driving torque curve of the novel two-translational parallel mechanism is obtained.Finally,a prototype of the novel two-translational parallel mechanism is manufactured and the position control experiments based on inverse kinematics are performed,which can validate the rationality and feasibility of the mechanism.