# MapleSoft announces case studies and Maple T.A. update

Maplesoft has made several announcements regarding its Maple, MapleSim and Maple T.A. solutions. Firstly, the company has announced that engineers at Kinova Robotics, which designs and manufactures innovative robotics products for personal assistance and service functions, used Maple to derive and manage the complex matrix equations that underlie the advanced algorithms that control the JACO robotic arm, leading to improved functionality.

JACO features six interlinked segments - the last of which is a three-fingered hand – and operates with six degrees of freedom. With a reach of 90cm, it can be mounted onto a motorised wheelchair or a fixed base. Using a joystick controller, the user can move the robot’s hand in three-dimensional space to grasp and release objects as required, to perform routine tasks.

Kinova’s Robotic Algorithms and Control Team faced a key challenge in the design of the arm’s controller. In order to safely operate the robotic arm, they needed to design advanced algorithms involving large matrix equations to calculate the kinematics and applied forces through the arm. An added complexity is that these computations, which are run on a microcontroller, must be performed repeatedly, at very short time intervals. Therefore, the algorithms must be continuously refreshed at a rapid rate, which creates a very large matrix of simultaneous trigonometric equations.

Maple’s high-performance symbolic computation engine was deployed as it enables users to describe, visualise and solve complex mathematical problems. Using Maple, the first step was to define the inputs to the program – which included the number of links, their lengths, and the joint angles. After defining the relationships between these variables, they were able to create a system of trigonometric equations that represented the problem to be solved.

Then, the team used Maple’s symbolic computation engine to analyse and simplify these equations to generate the output function, which calculates the position of the hand. This optimised output function – still in its symbolic form – was then converted into C++ code for use in simulation, and in the arm’s embedded controller.

In further news, in the mining industry, FLSmidth engaged the services of Maplesoft´s Engineering Solutions team to develop design and analysis tools that would help them design a Dual Truck Mobile Sizer (DTMS) – an innovative machine that can be relocated throughout a project, as the haul distances increase. To create tools that would help FLSmidth to design this equipment, the Maplesoft team first had to develop a deep understanding of the dynamics of the skip system. They began by using MapleSim, the advanced modelling and simulation platform, to develop a fully parameterised model of the skip. Taking advantage of MapleSim´s multidomain modelling capabilities, they were able to create a high-fidelity model that incorporated all the key components of the skip – from its geometric structure and mechanical operation, to the hydraulic circuits and controllers.

The creation of the skip model was complemented with the development of multiple design tools to aid in adjusting the model to achieve the desired behaviour. One such design tool is the Geometric Design Evaluation tool, which provides the ability to evaluate changes in the dimensions of the skip design and their effect on the dynamics of the system. The tool uses Maple – Maplesoft´s symbolic computation tool – to perform a parameter sweep, by simultaneously running simulations using the different parameter values provided. Maple then presents the results overlaid on a single plot window for easy comparison and evaluation. Other tools developed include tools for sizing the hydraulics and components, designing the motion profile, investigating the dynamic loading on the bearings, and estimating the material flow load.

MapleSoft’s third announcement is that the company has updated Maple T.A., its online testing and assessment system designed for courses involving mathematics. Ideal for use in science, technology, engineering, and mathematics (STEM) courses, Maple T.A. now supports the Learning Tools Interoperability (LTI) standard. This means Maple T.A. can be easily integrated with course management systems that support LTI. Maplesoft officially supports LTI connectivity with Canvas, Blackboard Learn, Brightspace, Moodle, and Sakai.