# Linear Flexible Joint

## Introduce Control Concepts Related to Vibration Analysis and Resonance

The Linear Flexible Joint system is ideal to introduce intermediate control concepts related to vibration analysis and resonance. You can use it to demonstrate real-world control challenges encountered, for example, in elastic linkages and mechanical transmissions.

The Linear Flexible Joint module is used paired with the Linear Servo Base Unit (IP02). With this setup students learn how to:

• develop a mathematical model of the system using Lagrangian mechanics
• obtain a linear state-space representation of the open-loop system
• design a state-feedback controller to get the spring-driven cart to a desired position as quickly as possible, while minimizing the overshoot and residual vibration
• simulate the closed-loop system to ensure the specifications are met
• implement the controller and evaluate the system’s performance

## Expand the Linear Flexible Joint Experiment

You can further expand your experiment by mounting the Linear Flexible Joint on the Seesaw module (can be purchased separarately). With this setup, students can learn how to maintain the seesaw balance by driving the carts back and forth.

Linear Flexible Joint on Seesaw

In addition to teaching intermediate control concepts, Linear Flexible Joint can be used for research in various areas, including system inversion,  time optimization, nonlinear control, robust control, intelligent control and system identification.

How It Works

The Linear Flexible Joint module consists of a passive linear cart coupled to a Linear Servo Base Unit through a linear spring. The Linear Flexible Joint is made of solid aluminum and uses linear bearings to slide along the Linear Servo Base Unit ground stainless steel shaft. The joint position is measured using a rotary optical encoder whose shaft meshes with the track via a pinion. The system is supplied with two additional masses that can be mounted atop the cart.

As the Linear Servo Base Unit moves back and forth, the Linear Flexible Joint cart will naturally tend to oscillate. Using feedback control, one can attempt to attenuate these motions.

Quanser-developed ABET-aligned Courseware Included

The Linear Flexible Joint module comes with Quanser-developed courseware standardized for ABET evaluation criteria. The workbook with exercises, together with quick start resources, a comprehensive User Manual, pre-designed controllers and a system model allow you to get your lab running faster, saving months of time typically required to develop lab materials.

• High resolution optical encoder to sense cart position
• Easy-connect cables and connectors
• High quality aluminum and precision-crafted parts
• Fully compatible with MATLAB®/Simulink® and LabVIEW™
• Fully documented system models and parameters provided for MATLAB®, Simulink®, LabVIEWTM and Maple™
• Open architecture design, allowing users to design their own controller

Linear Flexible Joint on Seesaw Option:

• Linear Flexible Joint easily attaches to Seesaw
 Linear Flexible Joint cart (LFJC) mass 0.22 kg LFJC weight mass 0.125 kg LFJC dimensions (L x D x H) 10 cm x 14 cm x 12 cm Equivalent spring stiffness 142 N/m Spring assembly mass 0.145 kg Spring length 29.0 cm LFJC encoder resolution (in quadrature) 4096 counts/rev

Topics included in the Quanser-developed courseware:

Modeling Topics

• Derivation of dynamic model using Lagrange
• State-space representation
• Parameter estimation
• Model validation

Control Topics

• Vibration control
##### The Linear Flexible Joint can be also used to teach other topics that are not included in the Quanser-developed courseware.

To set up your Linear Flexible Joint workstation, you need additional components. Quanser engineers recommend:

 for MATLAB®/Simulink® users for LabVIEW™ users 1x Linear Servo Base Unit 1x Linear Servo Base Unit 1x Q2-USB data acquisition device¹ 1x VoltPAQ-X1 linear voltage amplifier 1x VoltPAQ-X1 linear voltage amplifier Quanser Rapid Control Prototyping toolkit software QUARC real-time control software and one of the following options: - 1x NI myRIO with 1x Quanser Terminal Board for NI myRIO - 1x NI CompactRIO controller² with 1x Quanser Q1-CRIO module - 1x NI M- or X-series data acquisition device³ with 1x Quanser NI Terminal Board

¹ alternatively, you can use Q8-USB, QPIDe or any equivalent NI DAQ device supported by QUARC
² NI cRIO-9074, or NI cRIO-9024 with cRIO-9113 or cRIO-9114 chassis
³ NI DAQ device must be supported by Quanser RCP toolkit. Alternatively, you can use Quanser Q2-USBQ8-USB, or QPIDe

### Other products you might be interested in

Active Suspension
Multi-DOF Torsion
Linear Flexible Joint with Inverted Pendulum