Coordinate system

Link

Motion relative to previous link

Matrixi−1Ai

S0

Platform

Fixed link

S1

Base (Geometric link)

Translation along the Z0-axis at height H

0A1 = A3(H)

S2

Joint S (Kinematic link)

Rotation around the Z1-axis at angle φ

1A2 = A6(φ)

S3

Joint S (Geometric link)

Translation along the X2-axis on sx

2A3 = A1(sx)

S4

Joint S (Geometric link)

Translation along the Z3-axis on sz

3A4 = A3(sz)

S5

Joint L (Kinematic link)

Rotation around the Y4-axis at angle ψ1

4A5 = A5(ψ1)

S6

Joint L (Geometric link)

Translation along the Z5-axis on lz

5A6 = A3(lz)

S7

Joint U (Kinematic link)

Rotation around the Y6-axis at angle ψ2

6A7 = A5(ψ2)

S8

Joint U (Geometric link)

Translation along the X7-axis on ux

7A8 = A1(ux)

S9

Joint U (Geometric link)

Translation along the Z8-axis on uz

8A9 = A3(uz)

S10

Joint R (Kinematic link)

Rotation around the X9-axis at angle θ1

9A10 = A4(θ1)

S11

Joint R (Geometric link)

Translation along the X10-axis on rx

10A11 = A1(rx)

S12

Joint B (Kinematic link)

Rotation around the Y11-axis at angle ψ3

11A12 = A5(ψ3)

S13

Joint B (Geometric link)

Translation along the X12-axis on bx

12A13 = A1(bx)

S14

Joint T (Kinematic link)

Rotation around the X13-axis at angle θ2

13A14 = A4(θ2)

S15

Joint T (Geometric link)

Translation along the X14-axis on tx

14A15 = A1(tx)