Robotics Engineering

Articulated Robot Joint Repeatability Tolerance Allocation via Kinematic Sensitivity Calculator

Articulated Robot Joint Repeatability Tolerance Allocation via Kinematic Sensitivity engineering calculator.

Quick Answer

Calculate Articulated Robot Joint Repeatability Tolerance Allocation via Kinematic Sensitivity

Calculator

Joint j Repeatability Tolerance Allocation (m)
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Result Interpretation

Articulated Robot Joint Repeatability Tolerance Allocation via Kinematic Sensitivity Calculator computes Joint j Repeatability Tolerance Allocation in m using the defined engineering formula and the input values provided.

Worked Example

Verified calculation

Given:

  • L2 Norm of Jacobian Column for Joint j = 0.1
  • Total End-Effector Positional Repeatability = 0.0001
  • Sum of Squared L2 Norms of All Jacobian Columns = 0.025

Expected Result:

  • Joint j Repeatability Tolerance Allocation = 6.3245553203368E-5

Engineering Interpretation:

Under the given input conditions, the calculated result is: Joint j Repeatability Tolerance Allocation = 6.3245553203368E-5 m.

The actual numerical result is computed by the Runtime engine using the persisted tool definition. The values shown here come from automatically validated test cases.

Formula / Method

joint j repeatability tolerance allocation = total end-effector positional repeatability * (sqrt(pow(l2 norm of jacobian column for joint j, 2) / sum of squared l2 norms of all jacobian columns))

Formula family: formula_robotics_articulated_robot_joint_repeatability_budget_allocation_calculator

Variables

SymbolLabelRoleDescription
total_end_effector_repeatability Total End-Effector Positional Repeatability INPUT Total End-Effector Positional Repeatability
jacobian_column_norm_j L2 Norm of Jacobian Column for Joint j INPUT L2 Norm of Jacobian Column for Joint j
sum_of_squared_jacobian_column_norms Sum of Squared L2 Norms of All Jacobian Columns INPUT Sum of Squared L2 Norms of All Jacobian Columns
joint_repeatability_tolerance_allocation Joint j Repeatability Tolerance Allocation OUTPUT Joint j Repeatability Tolerance Allocation

Calculation Steps

  1. Enter the total end-effector positional repeatability in m.
  2. Enter the l2 norm of jacobian column for joint j in m/rad.
  3. Enter the sum of squared l2 norms of all jacobian columns in m²/rad².
  4. Step 1: Compute joint j repeatability tolerance allocation.
  5. Read the joint j repeatability tolerance allocation (m) from the results.

Engineering Summary

Calculate Articulated Robot Joint Repeatability Tolerance Allocation via Kinematic Sensitivity

Frequently Asked Questions

What does this calculator calculate?

The Articulated Robot Joint Repeatability Tolerance Allocation via Kinematic Sensitivity Calculator estimates Joint j Repeatability Tolerance Allocation based on the input parameters you provide

Why is total end-effector positional repeatability important in this calculation?

total end-effector positional repeatability is directly proportional to joint j repeatability tolerance allocation. When you enter total end-effector positional repeatability in m, the calculator uses it in the engineering formula to compute the output

How should I interpret the result joint j repeatability tolerance allocation?

The calculator outputs joint j repeatability tolerance allocation in m. The result is computed directly from the input values using the defined engineering formula

What units should I use for the inputs?

Enter each value in the units shown next to the input field: Total End-Effector Positional Repeatability (m), L2 Norm of Jacobian Column for Joint j (m/rad), Sum of Squared L2 Norms of All Jacobian Columns (m²/rad²). Make sure all inputs use the specified units for consistent results

What assumptions does this calculator use?

This calculator uses automatically validated engineering formulas. Results are approximate and should be validated against site-specific conditions, applicable codes, and professional engineering judgment

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