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Lift Force Improvements for the Micromechanical Flying Insect ∗ Lift Force Improvements for the Micromechanical Flying Insect ∗ S. Avadhanula†,R.J.Wood†,E.Steltz†,J.Yan‡,R.S.Fearing† †{srinath, rjwood, ees132, ronf}@eecs.berkeley.edu ‡ [email protected] †Department of EECS, University of California, Berkeley, CA 94720 ‡Department of ECE, University of British Columbia, Vancouver, Canada V6T 1Z4 Abstract Early work on the MFI proposed a flexible (or ac- cordion shaped) wing to generate these 2 DOF [4]. This paper presents some recent improvements in Later, a rigid wing approach was adopted to generate the fabrication and control of the Micromechanical Fly- better aerodynamic forces and to enable easier fabri- ing Insect (MFI), a centimeter sized aerial vehicle cur- cation. A detailed dynamic model of the mechanism rently being developed at the University of California, was derived and a framework for optimizing the var- Berkeley. We report a lift of 506µN from a single ious fabrication parameters based on this model was wing, which is sufficient for a 100 mg machine to lift constructed [9]. At the time however, limitations in itself off the ground. This lift matches very well with fabrication technology limited the performance of the predictions based on quasi steady state models. We structures. present some recent improvements in thorax fabrica- This report summarizes the improvements in vari- tion leading to the development of a light weight plat- ous performance parameters for the MFI. Section 2 de- form (≈ 100 mg), which generates 400µN of lift with a scribes the improvements to the structural dynamics single wing. We also present a new sensor mechanism from an improved wing differential design. Section 3 which makes it possible to sense the motion of the ac- describes a flight force measurement experiment and tuators without having to add anything to the structure compares the measurement to predictions by a quasi itself. steady state model. Section 4 presents a technique for directly measuring the lift and thrust forces of the 1 Introduction newest version of the MFI. Section 5 describes a new sensor mechanism which enables the external measure- ment of actuator (and wing) displacements and de- Micro Aerial Vehicles (MAV) are an attractive plat- scribes how this sensor can be used to estimate the form for sensor deployment, search and rescue, recon- wing damping for the MFI. naissance etc. because of their very small size and high maneuverability. Early work on microrobotic flight 2 Improvements in Thorax Dynamics was done by Shimoyama et al [1], while various aspects and approaches to micro aerial flight are being pursued The major mechanical component of the MFI is by various groups [3, 6]. The Micromechanical Flying the thorax which consists of two fourbar mechanisms Insect (MFI) project at UC Berkeley aims at build- which amplify the motion from the piezo electric ac- ing one such MAV with a wing span of about 25 mm tuators and a spherical wing differential mechanism to and weighing about 100 mg. Fundamental work by convert these amplified motions into wing flapping and Dickinson et al [2, 7] showed that insects depend on rotation. One of the major recent improvements in the a complex interaction of unsteady state aerodynamics thorax is a change in the basic structure of the wing to generate the necessary forces for lift and maneuver- differential. Previously, the wing differential consisted ability. In order to generate these forces, they showed of a modification to the basic spherical four-bar mecha- that insect wings must be capable of 2 degrees of free- nism using a spherical joint composed of three flexures dom (DOF) called flapping and rotation. For sufficient as shown in Fig. 1(a). Because this mechanism uses a forces, the wing must be able to go through about 120◦ ◦ larger number of flexures, it is able to tolerate greater of flapping and about 90 of rotation. fabrication misalignments without jamming, but suf- ∗This work was funded by ONR MURI N00014-98-1-0671 fers from too much stiffness. Recently, improved fab- and DARPA. rication techniques with much better precision have 1 enabled the use of proper spherical four-bars consist- a high inertia. The present generation of the MFI, ing solely of single DOF flexural joints (See [16] for a whose performance is shown in Fig. 2(b), shows a re- treatment of spherical fourbars and [5] for a treatment markably low coupling, a high resonance and excellent of flexures). Since we use a smaller number of flexures, DC motion. Although these are predictions, they have serial stiffness is increased allowing for greater power been experimentally verified on various occasions. See transmitted into the wing. Fewer flexures to prestress [9] for one of the experiments which verified these pre- also means vastly improved fabrication times. dictions. θ2 250 τ θ 200 1 1 {τ θ 150 2 2 τ1 θ2 Flapping 100 {τ Axis Magnitude 2 θ1 1 φ 50 θ2 0 2 0 50 100 150 200 250 300 350 4 100 3 3 τ1 θ1 4 ψ 0 { τ φ ψ 2 θ2 −100 τ θ Ground 2 1 2 Wing { Phase −200 τ2 θ1 1 γ γ −300 3 γ −400 1 θ 0 50 100 150 200 250 300 350 γ Spherical 1 2 joint Frequency (Hz) θ1 (a) (a) (b) 500 τ −> θ 400 1 1 Figure 1: Improvement in Wing Differential Design (a) τ −> θ 2 2 The wing differential mechanism design in [9] (b) The 300 200 τ −> θ 1 2 new wing differential mechanism design. Magnitude 100 0 The dynamic behavior of the thorax however, re- 0 50 100 150 200 250 300 350 mains the same as before because the change only 0 τ −> θ manifests itself as a (favorable) lower differential stiff- 1 1 −100 τ −> θ ness without affecting anything else. This model was 2 2 −200 × τ −> θ derived in [8, 9] and consists of a coupled 2 2 matrix Phase 1 2 which links the fourbar actuations (torques) to wing −300 −400 motion. 0 50 100 150 200 250 300 350 Frequency (Hz) (b) θ1 G11(s) G12(s) τ1 = (1) θ2 G21(s) G22(s) τ2 Figure 2: Predicted Frequency responses. (The magni- =: G(s) tudes shown are the peak-peak wing displacements at 150V) (a) Thorax constructed in May 2002 (b) Thorax The diagonal terms of this transfer function are the constructed in March 2003. drive transfer functions, while the off diagonal terms represent coupling between the fourbars through the Table 1 shows the evolution of the inertial compo- wing differential. Ideally, we like the two drive trans- nents of the MFI thorax over the past 2 years which fer functions to be identical and the coupling to be has a large part to play in the improved dynamics. Ta- negligible compared to the drive. ble 2 show the evolution of the predicted wing power Advances in the fabrication of the fourbar and dif- for the MFI based on its performance. ferential reported by Wood et al [10], have enabled these criteria to be met with much greater success 3 Flight Force Measurement than previous generations of the MFI which used a µ-origami approach proposed in [14]. As a compar- 3.1 Quasi Steady State Analysis ison, consider the behavior of the structure reported in [9] shown in Fig. 2(a), which shows a very coupled Schenato et al. [12] and Sane and Dickinson [7] have system arising from a large differential stiffness and derived a framework for calculating the expected wing 2 12µm SS 6µm SS 40µm CF xˆ0 which varies linearly from zero at the leading edge (Aug 01) (Jan 02) (Sep 02) to unity at the trailing edge: Actuators 3 3 3 3 Fourbar 30 15 10 Crot = π − xˆ0(r) (5) Differential 10 8 8 4 Wing 21 17 8 It is important to note here thatx ˆ0 is usually taken Total 60 43 29 to be a constant but this does not seem to adequately consider how the position of the blade element relative Table 1: Evolution of thorax inertia parameters to the rotation axis changes the force so it has been (mg-mm2) (The first row describes the major struc- written here explicitly as a function of r. tural material at various stages of the project which changed from stainless steel (SS) to carbon fiber (CF).) Wing Resonance Wing Power Aug 2001 100 Hz 1.5 mW Jan 2002 120 Hz 2.3 mW Sep 2002 160 Hz 3mW Table 2: Evolution of MFI wing beat frequency and power forces using a quasi-steady state model which assumes (a) Geometry of MFI wing (b) Carbon Fiber that the force equations derived for 2D thin aerofoils Differential and also hold for time varying 3D flapping wings. Yan Wing and Fearing [13] have adapted this model to the MFI Figure 3: Wing shape. wings accounting for the specific wing morphology of the MFI and the fact that the MFI kinematics is not In our setup, the body is stationary so this simplifies identical to insect wing kinematics as far as rotational the force estimate as there are no body dynamics to axes go. This method is briefly outlined here. For the consider. Setting U(t, r)=φ˙f (t)r, equations (2)-(4) wing shown in Fig. 3(a), the instantaneous differential can be integrated: force contributions from a vertical wing blade element of thickness dr at a distance r from the wing pivot are 2 ρCN (φr(t))φ˙f (t) given as follows: Ftr,N (t)= I (6) 2 2 2 CN (φr(t))ρc(r)U (t, r)dr ρCT (φr(t))φ˙f (t) dF (t, r)= (2) Ftr,T (t)= I (7) tr,N 2 2 2 CT (φr(t))ρc(r)U (t, r)dr Frot,N (t)=ρπφ˙r(t)φ˙f (t)I˜ (8) dF (t, r)= (3) tr,T 2 2 ˙ where I is the second moment of area of the wing about dFrot,N(t, r)=Crotρc (r)φrU(t, r)dr (4) axis A and where the “tr” and “rot” subscripts indicate whether 3 2 the contribution is due to translational or rotational I˜ = − xˆ0(r) c (r)rdr (9) 4 motion, the “N” and “T” subscripts indicate that the direction is either normal or tangential to the wing (no- The wing of Fig.
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