Topology optimization of three-translational degree-of-freedom spatial compliant mechanism

Abstract

Considering that the Jacobian matrix maps the velocity of the joint space of the robot to the end velocity of the Cartesian space, a novel topology optimization approach is proposed in this article for the design of three-translational degree-of-freedom spatial compliant mechanisms by combining the optimized Jacobian mapping matrix with the solid isotropic material with penalization topological method. First, by using the condition number method, the structural parameters of Universal-Prismatic-Universal (UPU)-type parallel prototype manipulator are optimized, and then, the differential Jacobian mapping matrix is calculated by using equivalent infinitesimal method. Second, comparing with the driver configuration and twist/wrench constraint conditions of the UPU-type parallel prototype manipulator, the topological algorithm combining solid isotropic material with penalization with optimized Jacobian mapping matrix is proposed. Finally, a novel spatial compliant mechanism with three-translational degree-of-freedom is derived, and numerical simulation results are reported to demonstrate the effectiveness of the proposed method.

Optimization design of compliant focusing mechanism for space optical camera with light weight

“…The interaction force F r can be obtained by solving equation (12). Then, F r is substituted into equations ( 1), ( 3), ( 4), ( 9), (10), and (11). Based on the above information, u in and u out can be respectively derived from equations (7) and (6).…”

“…9 A micro gripper based three-stage amplified compliant mechanism actuated by the PZT was achieved to grip the micro parts by Chen et al 10 It can be seen that the compliant mechanism is the better choice to design the high-precision focusing mechanism. 11,12 In virtue of the larger output force, higher stiffness and fast response speed, the PZT actuator is usually used for ultra-precision motion and positioning. 13 However, the output displacement of the PZT actuator is more small and cannot achieve the design requirements of large strokes.…”

A Review on Tailoring Stiffness in Compliant Systems, via Removing Material: Cellular Materials and Topology Optimization

“…Later, Jin et al [202] enhanced their previous research by including an improved stiffness evaluation generating new optimal compliant limbs and thus compliant parallel mechanisms (see Figure 12(b-ii,c-ii) that have better levels of off-axis stiffness, and are similar to the generated in their previous work. Most recently, a different technique, not applied at the flexure level, has been used to design the limbs of compliant parallel platforms; this is based on keeping the mobile and fixed platforms as rigid bodies while applying a Topology Optimization process on a design domain that connects both platforms, examples using this technique designing 2D and 3D compliant parallel platforms can be found in [203][204][205][206], respectively. Topology Optimization of single flexures, i.e., those that are not part of a compliant mechanism, has been also addressed.…”

Multi-material topology optimization of large-displacement compliant mechanisms considering material-dependent boundary condition

“…Topology optimization is the process of seek the best material distribution in a predefined domain, such that the obtained optimal topologies satisfy the required performance. 10 To date, several topology optimization approaches have been developed, such as ground structure method, 11,12 solid isotropic material with penalization method (SIMP), 13,14 level set method, 15,16 evolutionary structural optimization method 17,18 and moving morphable components. 19,20 Originally, topology optimization was applied to design the structures for maximizing stiffness.…”