Abstract
Compliant mechanisms are widely used for instrumentation and measuring devices for their precision and high bandwidth. In this paper, the mechatronic model of a compliant 3PRS parallel manipulator is developed, integrating the inverse and direct kinematics, the inverse dynamic problem of the manipulator and the dynamics of the actuators and the control. The kinematic problem is solved, assuming a pseudo-rigid model for the deflection in the compliant revolute and spherical joints. The inverse dynamic problem is solved, using the Principle of Energy Equivalence. The mechatronic model allows the prediction of the bandwidth of the manipulator motion in the 3 degrees of freedom for a given control and set of actuators, helping in the design of the optimum solution. A prototype is built and validated, comparing experimental signals with the ones from the model.
Highlights
The use of compliance in mechanisms has become very common for several purposes
While continuum mechanisms present slender elements that deflect along their whole length, compliant mechanism are composed of rigid elements joined by flexure hinges that deform under the application of a load [1,2]
With 3 degrees of freedom, an ultra-precision XYθz flexure stage with nanometric accuracy is presented in [9], and a cartesian XYZ compliant mechanism is designed in [10]. Another high-performance three-axis serial-kinematic nano-positioning stage for high-bandwidth applications is developed in [11], and in [12], where a large range modular XYZ compliant parallel manipulator is presented, where the structure is composed by identical spatial double four-beam modules
Summary
The use of compliance in mechanisms has become very common for several purposes. Compliant and continuum mechanisms make use of the flexibility of some parts of the mechanism to achieve motion with several degrees of freedom. With 3 degrees of freedom, an ultra-precision XYθz flexure stage with nanometric accuracy is presented in [9], and a cartesian XYZ compliant mechanism is designed in [10] Another high-performance three-axis serial-kinematic nano-positioning stage for high-bandwidth applications is developed in [11], and in [12], where a large range modular XYZ compliant parallel manipulator is presented, where the structure is composed by identical spatial double four-beam modules. All the theoretical considerations to develop the mechatronic model of the compliant 3PRS are thoroughly shown, mainly, the kinematics and the dynamics of both the manipulator and the control and actuators. Jacobians For the resolution of the inverse dynamic problem, the Jacobians of the different elements of the manipulator are required
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