Design of a Maximally Regular Acceleration Sensor Based on Generalized Gough-Stewart Platforms
An analytical formulation and a new routine are presented to design a maximally regular acceleration sensor based on a generalized Gough-Stewart platform. The Jacobian matrix considering the measuring point is constructed symbolically and also acceleratio
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Abstract An analytical formulation and a new routine are presented to design a maximally regular acceleration sensor based on a generalized Gough-Stewart platform. The Jacobian matrix considering the measuring point is constructed symbolically and also acceleration mapping matrix done. Optimal indices and coupling evaluation are proposed to qualify performances of the sensor. Subsequently, the singular values of the acceleration Jacobian matrix are solved analytically to evaluate acceleration transmission. The conditions for the maximally regular acceleration are expressed in close-form. Based on the analytical formulation, an optimal design routine is put forward to determine a family of orthogonal and maximally regular acceleration sensor. With the aid of numerical examples, the acceleration-coupling is investigated and the results illustrate that the proposed design method is effective.
Keywords Acceleration sensor Gough-Stewart platform hyperboloids Coupling analysis
Isotropy Circular
1 Introduction Gough-Stewart parallel manipulators have been employed in a wide variety of areas such as manipulation, matching, control, tracking, haptic force feed-back, etc. When considering the implementation of parallel mechanisms in the field of senZ. Tong (&) H. Jiang H. Zhang J. He Department of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150001, China e-mail: [email protected] H. Jiang e-mail: [email protected] H. Zhang e-mail: [email protected] J. He e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2017 X. Zhang et al. (eds.), Mechanism and Machine Science, Lecture Notes in Electrical Engineering 408, DOI 10.1007/978-981-10-2875-5_106
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sors, the Gough-Stewart structure has become an alternative solution for certain applications including force/torque sensors and acceleration sensors. An acceleration sensor with orthogonal or isotropic performance has better sensitivity and higher accuracy without doubt, however, it has been researched scarcely any. A lot of theoretical and experimental investigations on the 6-dof force/torque sensors with Gough-Stewart platforms were carried out in-depth by many researchers [1–5]. In general, few works focused on the 6-dof acceleration sensors with parallel structures. Xu et al. derived a symbolic expression to evaluate the acceleration isotropy of a Stewart platform-based acceleration sensor [6]. An E-type linear accelerometer with three dimensions was developed to measure the applied force from the upper limb [7]. However, the decoupling process was difficult and non-standard due to its unique and complex structure. To obtain a decoupled configuration with compact elements, Gao et al. presented a multidimensional acceleration sensor through the novel architecture of 3RRPRR fully decupling parallel mechanism [8]. For its special mechanism, only linear acceleration can be sensitive. Theoretically, orthogonality is interesting for geometry of mechanism; so many design approaches have been presented. J
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