MCT 4215

1. Explain the differences between "moving frames" and "fixed frames" approach in determining positions and orientations
-- Moving frame is "current frame", all transformations are post-multiplied (->). Fixed frame is "reference frame", all transformations are pre-multiplied (<-).

2. Forward and inverse mapping of RPY (Roll, Pitch, Yaw) angles of wrist of robot.
-- RPY(a,o,n): Rot(a) Rot(o) Rot(n)
-- Ta = atan2(ny,nx) / atan2(-ny,-nx)
-- To = atan2(-nz, (nxCta + nySta))
-- Tn = atan2(-ayCta+axSta, oyCta-oxSta)

3. Usage of sensors are used in a robotic.
- Position (LVDT), velocity, force (stress gauge), touch, tactile, proximity, range (ultrasonic/infrared), vision
- Cost, size, weight, output, interface, resolution
- 63.2% time constant, .1-.9 rise, 0-.98 settle
- CR differential, RC integral (op-amp)
- Proximity sensor (inductive - metal, capacitive - nonmental, eddy current)

4. Incremental encoder rating 2000pulse/rev attached with motor 1st joint. Reduction gear with ratio 4 between body and shaft. Calculate resolution angular displacement of arm. Any change of encoder replaced with 13-bit absolute encoder?
Pulse/deg = 2000/360
Deg/pulse = 0.18

13-bit absolute: 8192 position
Deg/position: 360/8192 = 0.044

5. In robotic system, gear reduction is required. Why? Differentiate Ieffective/Itotal.
- Higher torque, lower speed, manageable
- Decreased inertial load: Effective = Iload/N^2; Total = Iload/N^2 + Imotor

6. Hydraulic/Electric actuator in robot design
- Low vs avg power-to-weight
- High-maint vs low-maint
- Stiff vs less stiff
- No gear reduce vs reduce
- Inertial load vs less load (gear red.)
- Non-clean vs clean

7. Assign joint frames according to D-H algorithm. Tabulate D-H parameters. Derive A matrices for link 1-3.
-- DH = Rot(z,th)Trans(0,0,d)Trans(a,0,0),Rot(x,al)

8. Consider two frames A and C. Coordinate vector of a point P in the frame A is (a)P= [6 3 5]T. Find coordinate vector of point P in frame C.

9. Derive inverse kinematic equations for t1, t2, and t3 and symbolic form.
(Given 3 A-matrices and D-H representation)

C 0 S 0
S 0 -C 0
0 1 0 0
0 0 0 1

Revolute. Alpha = pi/2. a = 0.

C -S 0 LC
S C 0 LS
0 0 1 0
0 0 0 1

Revolute. Alpha = 0. a = L.

C -S 0 LC
S C 0 LS
0 0 1 0
0 0 0 1

Revolute. Alpha = 0. a = L.

10. Calculate t1, t2, t3 for following location. Length of each link L1,2,3 are 1, 2, 1.5ft.

T=
0.366	0.785	0.5		1.772
0.211	0.453	-.866	1.023
-.906	.422	0		-2.77
0		0		0		1