In order to execute geometric analysis for planar deployable mechanism of scissors unit,the dynamic analysis model of scissor planar deployable structure is created based on the Cartesian coordinate system,the influence coefficient is acquired by means of the coordinate transformation,combining the D 'Alembert 's principle with Dynamic-Static method,the dynamic characteristic analysis is completed finally. Moreover,specific calculating examples are adopted to verify the effectiveness of proposed method,and the result shows that the movement of each component of scissors unit mechanism is more smooth during initial deployment stage,however,when the configuration angle θ of unit mechanism is approaching π,some comparative large variations would appear on movement parameters and hinge constraint force.
The deployable mechanisms consisting of square units are widely applied in aeronautics and astronautics,biomedicine, architecture and other fields, and joint clearance in such a mechanism is unavoidable. This study is carried out to accurately investigate the dynamic property of the mechanism.Firstly,a dynamics model was built by considering the motion characteristics between elements of joint with clearances. Secondly,based on Floures contact force model and LuGre friction force model,the tangential and normal contact force of revolute pair element with clearance were calculated respectively. Finally,square combined mechanisms' dynamic analytical method considering joint clearance was investigated, and constraint renege problem was resolved by adopting Baumgarte stable constraint method in integration process.Analytical result indicates that the impact of joint clearance on dynamic property of square combined mechanism should not be neglected.
Because the deployable structures are complex multi-loop structures and methods of derivation which lead to simpler kinematic and dynamic equations of motion are the subject of research effort, the kinematics and dynamics of deployable structures with scissor-like-elements are presented based on screw theory and the principle of virtual work respectively. According to the geometric characteristic of the deployable structure examined, the basic structural unit is the common scissor-like-element（SLE）. First, a spatial deployable structure, comprised of three SLEs, is defined, and the constraint topology graph is obtained. The equations of motion are then derived based on screw theory and the geometric nature of scissor elements. Second, to develop the dynamics of the whole deployable structure, the local coordinates of the SLEs and the Jacobian matrices of the center of mass of the deployable structure are derived. Then, the equivalent forces are assembled and added in the equations of motion based on the principle of virtual work. Finally, dynamic behavior and unfolded process of the deployable structure are simulated. Its figures of velocity, acceleration and input torque are obtained based on the simulate results. Screw theory not only provides an efficient solution formulation and theory guidance for complex multi-closed loop deployable structures, but also extends the method to solve dynamics of deployable structures. As an efficient mathematical tool, the simper equations of motion are derived based on screw theory.
Bennett's linkage is a spatial fourlink linkage,and has an extensive application prospect in the deployable linkages.Its kinematic and dynamic characteristics analysis has a great significance in its synthesis and application. According to the geometrical conditions of Bennett 's linkage,the motion equations are established,and the expressions of angular displacement,angular velocity and angular acceleration of the followers and the displacement,velocity and acceleration of mass center of link are shown. Based on Lagrange's equation,the multi-rigid-body dynamic model of Bennett's linkage is established. In order to solve the reaction forces and moments of joint,screw theory and reciprocal screw method are combined to establish the computing method.The number of equations and unknown reaction forces and moments of joint are equal through adding link deformation equations. The influence of the included angle of adjacent axes on Bennett 's linkage 's kinematic characteristics,the dynamic characteristics and the reaction forces and moments of joint are analyzed.Results show that the included angle of adjacent axes has a great effect on velocity,acceleration,the reaction forces and moments of Bennett's linkage. The change of reaction forces and moments of joint are apparent near the singularity configuration.
