1 Introduction
2 Kinematics Analysis of the 2DOF SPM
2.1 Mobility Analysis
2.2 Inverse Kinematics of the SPM
2.2.1 Establishment of the Coordinate Systems
2.2.2 Description of the Configuration
2.2.3 Solutions of Coordinates with Configuration Parameters
2.2.4 Solutions of Coordinates with Driving Parameters
2.3 Forward Kinematics of the SPM
2.4 Jacobian Matrix Analysis
2.5 Verification of Kinematic Analysis
Institutional parameters of the initial configuration (°) | Tiny input θ21; θ61(°) | The theoretical value of Jacques φ, γ (×10-3 °/s) | The value of the CAD model ∆φ, ∆γ (×10-3 °/s) |
---|---|---|---|
θ21 = 14 | 0.001 | 3.4397 | 3.4417 |
θ61 = 23 | 0.002 | − 0.3657 | − 0.3505 |
φ = 59.0786 | − 0.003 | 0.9701 | 0.8857 |
γ = − 4.7420 | 0.004 | − 3.6240 | − 3.6368 |
θ21 = 31 | 0.001 | − 1.1911 | − 1.2617 |
θ61 = 12 | − 0.002 | 1.5686 | 1.6108 |
φ = 64.9472 | − 0.003 | 1.4643 | 1.6035 |
γ = 9.2984 | 0.004 | − 3.5059 | − 3.5913 |
3 Workspace Analysis
Limited configuration | φ (°) | \(\lambda\) (°) | Configuration of the mechanism |
---|---|---|---|
1 | 49.8502 | − 67.5085 | |
2 | 49.8502 | 67.5085 | |
3 | 95.8430 | 0 | |
4 | 11.5519 | 0 |
4 Equivalent Rotation Characteristics of the Mechanism
4.1 Equivalent Rotation Characteristics
4.2 How to Realize the Equivalent Rotation
4.3 Motion Planning of the Equivalent Rotation
Configuration 1 (θ = 0°) | Configuration 2 (θ = 13°) | Configuration 3 (θ = 26°) | Configuration 4 (θ = 40°) | |
---|---|---|---|---|
Equation of rotation axis | \(\frac{x}{ - 0.7933} = \frac{y}{0.1257} = \frac{z}{ - 0.5957}\) | |||
Institutional configuration φ, γ | φ = 75° γ = − 20° | φ = 74.5° γ = − 7.1° | φ = 72.9° γ = − 5.8° | φ = 70° γ = 20° |
Driving angle | θ21 = 5.3° θ61 = 56.7° | θ21 = 18.3° θ61 = 35.3° | θ21 = 32.3° θ61 = 18.9° | θ21 = 49.2° θ61 = 3.7° |