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Research Papers

Joint Angle Measurement Using Strategically Placed Accelerometers and Gyroscope

[+] Author and Article Information
Vishesh Vikas

Center of Intelligent Machines
and Robotics (CIMAR),
Department of Mechanical and
Aerospace Engineering,
University of Florida,
Gainesville, FL 32611
e-mail: vishesh.vikas@gmail.com

Carl D. Crane, III

Center of Intelligent Machines
and Robotics (CIMAR),
Department of Mechanical and
Aerospace Engineering,
University of Florida,
Gainesville, FL 32611
e-mail: carl.crane@gmail.com

1Current affiliation: Postdoctoral Researcher, Neuromechanics and Biomimetic Devices Laboratory, Tufts University, Meford MA 02155.

Manuscript received November 26, 2014; final manuscript received July 25, 2015; published online November 24, 2015. Assoc. Editor: Jaydev P. Desai.

J. Mechanisms Robotics 8(2), 021003 (Nov 24, 2015) (7 pages) Paper No: JMR-14-1328; doi: 10.1115/1.4031299 History: Received November 26, 2014; Revised July 25, 2015; Accepted July 26, 2015

Optical and magnetic encoders are widely used to measure joint angles. These sensors are required to be installed at the axes of rotation (joint centers). However, microelectromechanical system (MEMS) accelerometer and gyroscope-based joint angle measurement sensors possess the advantage of being flexible with regard to the point of installation. Inertial measurement units (IMUs) are capable of providing orientation and are also used for joint angle estimation. They conventionally fuse gyroscope and accelerometer data using Kalman filter-like algorithm to estimate the joint angles. This research presents a novel approach of measuring joint parameters—joint angles, angular velocities, and accelerations, of two links joined by revolute or universal joint. The gravity-invariant vestibular dynamic inclinometer (VDI) and planar VDI (pVDI) are used on each link to measure the joint parameters of links joined by revolute and universal joints, respectively. The VDI consists of two dual-axis accelerometers and an uniaxial gyroscope, while the pVDI consists of four strategically placed dual-axis accelerometers and a triaxial gyroscope. The measurements of joint parameters using the presented algorithms are independent of integration errors/drift, do not require knowledge of robot dynamics, and are computationally less burdensome.

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Figures

Grahic Jump Location
Fig. 6

Modeling of the joint as a universal joint (Euler 2-1 angles): (a) the base and link joined at point O and (b) links i, j joined at point Oi,j

Grahic Jump Location
Fig. 11

Comparison of Euler 2-1 angles of the universal joint with the readings from the magnetic encoder

Grahic Jump Location
Fig. 5

Other possible variations in the pVDI sensor design. The two different planes that the accelerometers may be placed symmetrically are the (a) {e2,e3} or (b) {e3,e1} plane. The hollow arrows indicate the measurement directions of the dual-axis linear accelerometers.

Grahic Jump Location
Fig. 4

The design of the pVDI consists of a triaxial gyroscope (G) and four symmetrically placed accelerometers along e1 and e2 directions about point P. Hollow arrows indicate the direction of the required measurements.

Grahic Jump Location
Fig. 3

The VDI and pVDI sensors can be concisely presented as a function which, when given the location of the sensor from the joints (rPi/Oh,i, rPi/Oi,j), calculates the linear acceleration of the two joints (aOh,i, aOi,j), angular velocity (ωLI) and acceleration (αLI) of the link

Grahic Jump Location
Fig. 2

The VDI is comprised of two accelerometers (L, R) and a gyroscope (G). Three different designs for placement of the accelerometers are possible: (a) accelerometers are symmetrically placed at distance d/2 about point P along axis e1. (b) Here the accelerometers are placed symmetrically along axis e3. (c) Design of VDI where the accelerometers are nonsymmetrically placed about point P.

Grahic Jump Location
Fig. 1

Mechanism comprises rigid links where each link has an inertial sensor combination attached onto it at some location. (a) Two links i, j are joined at point Oi,j. The joint Oi,j may be modeled as a revolute (joint angle between links) or universal joint (Euler joint angles between links). (b) The base link is in contact with the ground surface with acceleration g at one end (Ob). The base angle(s) represent the angle(s) between g and the link b.

Grahic Jump Location
Fig. 7

Experimental setup of two links (L1, L2) joined by an universal joint. Each link has a pVDI sensor (pVDI1, pVDI2) strapped onto it which consists of four symmetrically placed MEMS accelerometers and a MEMS gyroscope.

Grahic Jump Location
Fig. 8

Experimental setup of the pVDI sensor consisting of four symmetrically placed linear MEMS accelerometers at a distance of 6 cm from the centerline and one MEMS gyroscope

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Fig. 9

Comparison plot of angular acceleration of link 1 obtained from the pVDI sensor with differentiated values from smooth gyroscope readings

Grahic Jump Location
Fig. 10

Plot of angular acceleration of link 2 obtained from the pVDI sensor. The values are compared against differentiated gyroscope readings.

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