Skills

Mechanism Design and Kinematic Analysis

6 weeks · 0 milestones

Design a mechanism for a specific function and perform a complete kinematic analysis covering: a kinematic diagram showing all links, joints, and degrees of freedom with Gruebler's criterion applied, position analysis (at least 3 positions in the motion cycle), velocity and acceleration analysis for the critical position, force analysis under the specified load, and identification of any design constraints or singularities (positions where the mechanism locks or becomes indeterminate). The mechanism must be non-trivial — at least a 4-bar linkage or equivalent complexity. Preferred proof: a mechanism designed for a real application with physical prototype evidence. Accessible alternative: kinematic analysis of a documented mechanism scenario using FreeCAD's kinematic analysis module or hand calculation with velocity polygon diagrams — equivalent rigor required. Proof artifacts: the kinematic diagram and analysis (design artifact) and the force analysis results with documented methodology (analysis artifact). Verification: a mechanical engineer reviews the kinematic analysis — 'what is the mechanical advantage at this position, and how does it change across the motion cycle?' — requiring you to reason from your own analysis.

Part of: Engineering · Proves for: Engineers, UG

Milestone map

3 milestones

Define the Mechanism and Establish Kinematic Model

1–2 weeks (3–4 hrs/week)

Select a mechanism to analyse — a four-bar linkage, slider-crank, cam-follower, gear train, or similar multi-body system. Draw the kinematic schematic: links, joints, degrees of freedom. Compute the degree of freedom (Grübler's equation) and confirm the mechanism is correctly constrained. Sketch the positions at ≥3 key configurations (e.g. dead-centre, mid-stroke, fully extended) to build intuition before formal analysis.

Proof required

Submit your kinematic model document: the mechanism description, kinematic schematic diagram with labelled links and joints, Grübler's calculation confirming degrees of freedom, and position sketches at ≥3 configurations.

What gets checked

Kinematic schematic labels every link with a number and every joint with a type (revolute, prismatic, cam, etc.)
Grübler's equation is applied and shows the correct degree of freedom — 1 for a single-input mechanism
Position sketches at ≥3 distinct configurations are included and labelled

Common mistakes

Drawing an assembly diagram rather than a kinematic schematic — kinematic schematics show only links and joints, not part geometry
Skipping the Grübler check — a mechanism with the wrong degree of freedom count cannot be correctly analysed

Resources

Foundationstart here

Depthgo deeper

What a verifier looks for

Confirm kinematic schematic shows only links and joints — not 3D geometry or assembly details.
Confirm Grübler's equation is applied with all terms shown — links, joints, and degree of freedom result stated.
Confirm position sketches show ≥3 distinct configurations with labels.

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Perform Velocity and Acceleration Analysis

3–4 weeks (4–5 hrs/week)

Using graphical (velocity polygon, acceleration polygon) or analytical (vector loop equations) methods, calculate the velocity and acceleration of key points in the mechanism across a full cycle of motion. Plot velocity and acceleration versus crank angle (or input position) for at least one output point. Identify the position of maximum velocity and maximum acceleration — these govern the dynamic loads in downstream force analysis.

Proof required

Submit your kinematic analysis: velocity and acceleration calculations for ≥5 crank angle positions, clearly showing method (graphical or analytical), and velocity/acceleration vs. crank angle plots for at least one output point.

What gets checked

Calculations show all steps — input values, intermediate results, and output values — not just final numbers
Velocity and acceleration plots cover a full 360° cycle and identify the maximum values with their crank angle positions
Analysis method (graphical or analytical) is stated and applied consistently throughout

Common mistakes

Analysing only one or two positions — five positions minimum are needed to produce a meaningful plot of the kinematic cycle
Using graphical polygons without checking the velocity scale — scale errors in graphical methods produce incorrect magnitude results

Resources

Foundationstart here

Depthgo deeper

What a verifier looks for

Confirm calculations are shown for ≥5 crank angle positions — not just a final plot without intermediate work.
Confirm velocity and acceleration plots cover a full 360° cycle.
Confirm maximum values are identified with their crank angle positions.

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Apply Dynamic Force Analysis and Document Results

2–3 weeks (3–4 hrs/week)

Using the acceleration results from M2, perform a dynamic force analysis of the mechanism. Apply Newton's second law to each link (F = ma for translation, M = Iα for rotation) to find the reaction forces at each joint. Summarise the design implications: which joint carries the highest force, what is the required bearing capacity at each joint, and how does the force magnitude vary over the cycle. Write a complete kinematic analysis report and have it reviewed by a mechanical engineer.

Proof required

Submit your dynamic force analysis (all calculation steps shown) and kinematic analysis report (≥1,500 words): mechanism description, kinematic model, velocity/acceleration analysis summary, dynamic force results, design implications, and review record (reviewer name, role, ≥3 challenge questions, responses).

What gets checked

Dynamic force analysis applies Newton's second law to each link with the acceleration magnitudes from M2 — not assumed or estimated forces
Design implications name the highest-loaded joint and state the required bearing capacity
Review record names the reviewer, their mechanical engineering background, and documents ≥3 specific technical challenge questions

Common mistakes

Reporting maximum joint forces without identifying which configuration produces them — the design must know when the worst-case loading occurs
Reviewer without kinematics or dynamics background — challenge questions must probe the force analysis method, not just the report writing

Resources

Foundationstart here

Depthgo deeper

What a verifier looks for

Engineering Design Triad check: M1–M3 together produce a design artifact (kinematic schematic + mechanism model), an analysis artifact (velocity/acceleration analysis + dynamic force calculations), and a documentation artifact (kinematic analysis report + review record) — confirm all three types are present.
Confirm dynamic force analysis applies Newton's second law with the acceleration magnitudes from M2 — not estimated static forces.
Confirm design implications name the critical joint and state the bearing capacity requirement.
Confirm reviewer has mechanical engineering background and review record documents specific technical challenge questions.
The Proof Accessibility Rule applies — GeoGebra (free), Python/matplotlib (free), MIT OCW (free), FreeCAD (free), and Open Library textbooks are all accessible without institutional licence.

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Part of

Mechanical Engineering →

Related outcomes

Milestone map

3 milestones

Define the Mechanism and Establish Kinematic Model

1–2 weeks (3–4 hrs/week)

Proof required

What gets checked

Kinematic schematic labels every link with a number and every joint with a type (revolute, prismatic, cam, etc.)
Grübler's equation is applied and shows the correct degree of freedom — 1 for a single-input mechanism
Position sketches at ≥3 distinct configurations are included and labelled

Common mistakes

Drawing an assembly diagram rather than a kinematic schematic — kinematic schematics show only links and joints, not part geometry
Skipping the Grübler check — a mechanism with the wrong degree of freedom count cannot be correctly analysed

Resources

Foundationstart here

Depthgo deeper

What a verifier looks for

Confirm kinematic schematic shows only links and joints — not 3D geometry or assembly details.
Confirm Grübler's equation is applied with all terms shown — links, joints, and degree of freedom result stated.
Confirm position sketches show ≥3 distinct configurations with labels.

You'll sign in first, then come straight back here.

Perform Velocity and Acceleration Analysis

3–4 weeks (4–5 hrs/week)

Proof required

What gets checked

Calculations show all steps — input values, intermediate results, and output values — not just final numbers
Velocity and acceleration plots cover a full 360° cycle and identify the maximum values with their crank angle positions
Analysis method (graphical or analytical) is stated and applied consistently throughout

Common mistakes

Analysing only one or two positions — five positions minimum are needed to produce a meaningful plot of the kinematic cycle
Using graphical polygons without checking the velocity scale — scale errors in graphical methods produce incorrect magnitude results

Resources

Foundationstart here

Depthgo deeper

What a verifier looks for

Confirm calculations are shown for ≥5 crank angle positions — not just a final plot without intermediate work.
Confirm velocity and acceleration plots cover a full 360° cycle.
Confirm maximum values are identified with their crank angle positions.

You'll sign in first, then come straight back here.

Apply Dynamic Force Analysis and Document Results

2–3 weeks (3–4 hrs/week)

Proof required

What gets checked

Dynamic force analysis applies Newton's second law to each link with the acceleration magnitudes from M2 — not assumed or estimated forces
Design implications name the highest-loaded joint and state the required bearing capacity
Review record names the reviewer, their mechanical engineering background, and documents ≥3 specific technical challenge questions

Common mistakes

Reporting maximum joint forces without identifying which configuration produces them — the design must know when the worst-case loading occurs
Reviewer without kinematics or dynamics background — challenge questions must probe the force analysis method, not just the report writing

Resources

Foundationstart here

Depthgo deeper

What a verifier looks for

Engineering Design Triad check: M1–M3 together produce a design artifact (kinematic schematic + mechanism model), an analysis artifact (velocity/acceleration analysis + dynamic force calculations), and a documentation artifact (kinematic analysis report + review record) — confirm all three types are present.
Confirm dynamic force analysis applies Newton's second law with the acceleration magnitudes from M2 — not estimated static forces.
Confirm design implications name the critical joint and state the bearing capacity requirement.
Confirm reviewer has mechanical engineering background and review record documents specific technical challenge questions.
The Proof Accessibility Rule applies — GeoGebra (free), Python/matplotlib (free), MIT OCW (free), FreeCAD (free), and Open Library textbooks are all accessible without institutional licence.

You'll sign in first, then come straight back here.