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Table 3 Evaluation based on 15 arbitrary target points

From: Non-iterative geometric approach for inverse kinematics of redundant lead-module in a radiosurgical snake-like robot

Id

Target position (mm)

Actual tip point (mm)

Joint angles (rad)

Error values (mm)

e (mm)

X

Y

Z

X

Y

Z

θ 1

θ 2

θ 3

θ 4

X

Y

Z

1a

35.895

47.082

22.319

35.894

47.082

22.319

0.919

−0.434

  

−3.69−4

−4.85−4

−2.82−4

6.71−4

2a

11.162

32.623

−47.650

11.162

32.623

−47.649

1.241

1.113

  

−1.14−4

−3.34−4

7.16−4

7.98−4

3a

−20.562

−35.615

10.237

−20.562

−35.615

10.237

1.047

−2.948

  

1.14−4

1.98−4

−4.48−5

2.33−4

4a

−46.787

−33.441

−25.663

−46.787

−33.441

−25.663

−2.521

0.504

  

−1.77−4

−1.27−4

−1.20−4

2.49−4

5a

−17.643

34.559

45.263

−17.643

34.559

45.263

2.043

−1.020

  

−9.10−5

1.78−4

3.26−4

3.82−4

6

−23.033

44.716

16.960

−22.893

44.443

17.027

−3.075

−0.169

−2.306

−0.292

0.141

−0.274

0.067

0.315

7

95.978

20.201

−7.583

95.860

20.201

−7.581

0.907

0.072

−1.394

0.056

−0.118

0.000

0.002

0.118

8

−70.092

96.494

−13.310

−69.766

96.251

−13.143

2.518

−0.055

−0.663

0.361

0.327

−0.243

0.167

0.440

9

−40.512

21.263

−13.329

−40.436

21.237

−13.375

−2.424

0.131

−2.394

0.238

0.076

−0.026

−0.463

0.093

10

−102.447

−12.848

−7.496

−102.421

−12.852

−7.499

2.634

0.147

1.262

−0.060

0.026

−0.004

−0.003

0.027

11

4.644

28.145

10.142

4.502

28.553

10.194

2.7539

−0.102

−2.679

−0.201

−0.142

0.408

0.052

0.435

12

−42.313

−35.407

21.584

−41.716

−34.948

21.660

−1.324

−0.218

−2.205

−0.354

0.595

0.459

0.076

0.755

13

124.266

−26.778

−10.907

123.671

−26.808

−9.911

−0.333

0.159

0.239

−0.158

−0.596

−0.030

0.997

1.162

14

52.552

−106.386

11.648

52.513

−106.138

11.561

−0.735

−0.110

−0.760

−0.018

0.039

−0.248

0.087

0.266

15

29.670

104.466

19.317

29.723

103.418

20.022

1.765

−0.529

−1.020

0.500

0.054

−1.048

0.705

1.264

  1. a2-link-module