Robot Dynamics, Actuation and Contacts
Comprehensive university textbook unit covering fundamental principles, governing relationships, and engineering applications of Robot Dynamics, Actuation and Contacts.
§3.1 Newton–Euler balance for links
**OpenSTEM Mechanical Engineering · Book 12: Robotics and Automation · Unit 3: Robot Dynamics, Actuation and Contacts.** Educational draft. All worked numbers are illustrative unless stated otherwise; do not use the calculations alone to certify a physical robot or protective system.
§3.2 Lagrange formulation and energy
**OpenSTEM Mechanical Engineering · Book 12: Robotics and Automation · Unit 3: Robot Dynamics, Actuation and Contacts.** Educational draft. All worked numbers are illustrative unless stated otherwise; do not use the calculations alone to certify a physical robot or protective system.
§3.3 Motor and gear selection
**OpenSTEM Mechanical Engineering · Book 12: Robotics and Automation · Unit 3: Robot Dynamics, Actuation and Contacts.** Educational draft. All worked numbers are illustrative unless stated otherwise; do not use the calculations alone to certify a physical robot or protective system.
§3.4 Grasp force, friction and object variability
**OpenSTEM Mechanical Engineering · Book 12: Robotics and Automation · Unit 3: Robot Dynamics, Actuation and Contacts.** Educational draft. All worked numbers are illustrative unless stated otherwise; do not use the calculations alone to certify a physical robot or protective system.
§3.5 Collision impulse and compliant contact
**OpenSTEM Mechanical Engineering · Book 12: Robotics and Automation · Unit 3: Robot Dynamics, Actuation and Contacts.** Educational draft. All worked numbers are illustrative unless stated otherwise; do not use the calculations alone to certify a physical robot or protective system.
Step-by-Step Robotics and Automation Solutions
Three original questions connect calculations, definitions and interpretation. Open each solution to follow the reasoning.
Problem Statement: With I=0.060 kg·m² and angular acceleration 4 rad/s², an ideal isolated axis needs 0.24 N·m acceleration torque before gravity and friction. Reproduce the substitution on paper, carry units through each stage and check the scale with an independent estimate. Precision in displayed decimal places does not demonstrate precise knowledge of link lengths, accelerations, friction coefficients or camera calibration. If inputs are rounded or synthetic, the outputs inherit those limitations; do not label them as measured robot performance.
Worked Engineering Derivation:
**Traceable Verification audit.** Record firmware or model version, sensor calibration, test fixture revision and all rejected trials. Set acceptance thresholds before viewing the final traces. If a physical trial cannot be carried out safely, use simulation only and write the missing validation item explicitly. Extend the example by sweeping one independent input through a realistic range. Predict the qualitative trend before computing. Then change another input in a separate run; explain why changing both simultaneously would make causal interpretation weaker. Document any singular, discontinuous or saturating regime instead of hiding it by clipping a plot without explanation.
Problem Statement: An engineering practitioner analyzes a mechanical system governed by **Lagrange formulation and energy** under steady operational loading.
Worked Engineering Derivation:
For a single rigid link with I=0.08 kg·m², angular acceleration 2 rad/s² gives 0.16 N·m inertia torque in the gravity-free idealization. Reproduce the substitution on paper, carry units through each stage and check the scale with an independent estimate. Precision in displayed decimal places does not demonstrate precise knowledge of link lengths, accelerations, friction coefficients or camera calibration. If inputs are rounded or synthetic, the outputs inherit those limitations; do not label them as measured robot performance. **Dimensional Balance audit.** Perform a units check by substituting SI base units and showing both sides match. For angles, state that trigonometric functions expect radians unless explicitly converted. For probabilities, check output within [0,1], and for lengths or times reject negative values when the model defines only positive quantities. Extend the example by sweeping one independent input through a realistic range. Predict the qualitative trend before computing. Then change another input in a separate run; explain why changing both simultaneously would make causal interpretation weaker. Document any singular, discontinuous or saturating regime instead of hiding it by clipping a plot without explanation.
Problem Statement: For gear ratio 12, efficiency 0.80 and motor torque 0.15 N·m, output torque is 1.44 N·m under the assumed point-efficiency. Reproduce the substitution on paper, carry units through each stage and check the scale with an independent estimate. Precision in displayed decimal places does not demonstrate precise knowledge of link lengths, accelerations, friction coefficients or camera calibration. If inputs are rounded or synthetic, the outputs inherit those limitations; do not label them as measured robot performance.
Worked Engineering Derivation:
**Boundary Cases audit.** Check a zero-input limit, a typical operating point and a maximum planned input. Where derivatives exist, estimate local sensitivity to a 5% change. If the result changes sharply, prioritize a measurement of the sensitive parameter rather than increasing numerical precision elsewhere. Extend the example by sweeping one independent input through a realistic range. Predict the qualitative trend before computing. Then change another input in a separate run; explain why changing both simultaneously would make causal interpretation weaker. Document any singular, discontinuous or saturating regime instead of hiding it by clipping a plot without explanation.
Problem Statement: An engineering practitioner analyzes a mechanical system governed by **Grasp force, friction and object variability** under steady operational loading.
Worked Engineering Derivation:
For m=1 kg, μ=0.50 and upward acceleration 1 m/s², each jaw needs at least 10.81 N in the ideal symmetric model. Reproduce the substitution on paper, carry units through each stage and check the scale with an independent estimate. Precision in displayed decimal places does not demonstrate precise knowledge of link lengths, accelerations, friction coefficients or camera calibration. If inputs are rounded or synthetic, the outputs inherit those limitations; do not label them as measured robot performance. **Discretization audit.** Choose a simulation step that resolves the fastest physical phenomenon of interest. Check convergence with a smaller step and confirm that numerical artifacts do not explain apparent stability or contact behavior. Sampling rates must exceed the bandwidth of the phenomena they are claimed to detect. Extend the example by sweeping one independent input through a realistic range. Predict the qualitative trend before computing. Then change another input in a separate run; explain why changing both simultaneously would make causal interpretation weaker. Document any singular, discontinuous or saturating regime instead of hiding it by clipping a plot without explanation.
Problem Statement: An engineering practitioner analyzes a mechanical system governed by **Collision impulse and compliant contact** under steady operational loading.
Worked Engineering Derivation:
A 2 kg object stopped from 0.5 m/s experiences 1 N·s magnitude impulse regardless of how quickly it is stopped. Reproduce the substitution on paper, carry units through each stage and check the scale with an independent estimate. Precision in displayed decimal places does not demonstrate precise knowledge of link lengths, accelerations, friction coefficients or camera calibration. If inputs are rounded or synthetic, the outputs inherit those limitations; do not label them as measured robot performance. **Uncertainty audit.** Differentiate precision from accuracy: repeated values near one another may share a systematic offset. Use replicated trials and a calibration reference, and consider correlations when combining uncertainties. An error bound must be linked to a defined operating range. Extend the example by sweeping one independent input through a realistic range. Predict the qualitative trend before computing. Then change another input in a separate run; explain why changing both simultaneously would make causal interpretation weaker. Document any singular, discontinuous or saturating regime instead of hiding it by clipping a plot without explanation.