mae 435 chris cook jeffry walker joshua beverly miguel de rojas

5-DOF ANTHROPOMORPHIC

MANIPULATOR

MAE 435

Chris Cook

Jeffry Walker

Joshua Beverly

Miguel de Rojas

Types of Manipulators

Cartesian Gantry Cylindrical Spherical SCARA Anthropomorphic – Make of 59% in use

worldwide as of 2005 IFR report

Types of Manipulators

Welding Manipulator

Surgical Manipulator

5 Degrees of Freedom

Gripper End-Effector

Project Goals

5cm x 5cm x 5cm cube Placed within 6 in radial position Repeated TBD number of times

Servo Motor vs. DC Motor

Preliminary CalculationsJointMass=.939; %mass of joint (kg)ShaftMass=.113; %mass of shaft (kg)ShaftLength=.2032; %length of shaft (m)MotorOutput=.4862; %N-m output torque peak effectiveGearRation=132; %ratio of planetary gearboxLoadLifted=.34; %minimum mass to be picked up (kg)g=9.81; %gravity %effective forcesjf=JointMass*g;sf=ShaftMass*g;lf=LoadLifted*g;L=ShaftLength; %Joint TorquesJ1torque=lf*3*L+jf*L*(3+2+1)+sf*L*(2.5+1.5+.5);J2torque=lf*2*L+jf*L*(2+1)+sf*L*(1.5+.5);J3torque=lf*L+jf*L+sf*L*.5;

Torque (N-m)

Joint 1 14.277

Joint 2 7.2414

Joint 3 2.6622

Selected Motor

Cost Considerations

Midterm Status Update

Machining and assembly complete unless modifications become necessary

Inventor solid model complete unless modifications become necessary

Wiring is complete pending testing Computer code for the microcontroller is

in development Dynamics/Kinematics in development

Machining

Assembly

Assembly Complete

Solid Model

Forward Kinematics

Denavit-Hartenberg Parameters• 3 fixed-link parameters αi and ai: describe the Link i • di and θi : describe the Link’s connection

Forward Kinematicsi αi-1 ai-1 di θi

1 0 0 d1 θ1

2 90 0 d2 θ2

3 0 a2 d3 θ3 + 90

4 90 a3 d4 θ4

5 -90 a4 d5 θ5𝑇𝑖

𝑖−1 =

cos𝜃𝑖 −sin 𝜃𝑖 0 𝑎𝑖− 1

sin𝜃 𝑖cos𝛼𝑖 −1 cos𝜃 𝑖cos𝛼𝑖 −1 −sin 𝛼𝑖−1 −sin𝛼 𝑖−1𝑑𝑖

sin𝜃 𝑖 sin𝛼𝑖− 1 cos𝜃 𝑖 sin𝛼𝑖− 1 cos𝛼𝑖−1 cos𝛼 𝑖−1𝑑𝑖

0 0 0 1𝑇10 =

cos𝜃1 −sin 𝜃1 0 0sin𝜃1 cos𝜃1 0 00 0 1 𝑑10 0 0 1

𝑇21 =

cos𝜃2 −sin 𝜃2 0 𝑎10 0 −1 −𝑑2

sin𝜃2 cos𝜃2 0 00 0 0 1

𝑇32 =¿

𝑇43 =

cos𝜃4 − sin𝜃4 0 𝑎30 0 −1 −𝑑4

sin 𝜃4 cos𝜃4 0 00 0 0 1

𝑇54 =

cos𝜃5 −sin 𝜃5 0 𝑎40 0 1 𝑑5

−sin 𝜃5 −cos𝜃5 0 00 0 0 1

𝑇50 = 𝑇1

0 𝑇21 𝑇3

2 𝑇43 𝑇5

4

Inverse Kinematics

Goal: determine all the joint variables for a specific end-effector position and orientation

Feed this information to the controls

Inverse Kinematics

Determine the inverse kinematics starting from this equation

Wiring/Soldering

Motor Drivers

Closed-Loop Feedback Control

PID Controller (Proportional Integral Derivative)

Control Signal Filter

Motor Driver

Motor and Gearbox

Gantt Chart

5-DOF Manipulator

5-DOF Manipulator in Action 2:08

References 1. Siciliano, B., et al., Robotics

Modeling, Planning and Control. Advanced Textbooks in Control and Signal Processing2009: Springer.

2. Lee, C.S.G., Robot Arm Kinematics, Dynamics, and Control. Computer, 1982. 15(12): p. 62-80.

3. MathWorks MATLAB 4. Autodesk Inventor 5. Microsoft Office Suite