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Component degrees of freedom in Solidworks - Cell-by-Cell Formula Trace

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Sample Data

This data shows components and their degrees of freedom in six directions: three translations (X, Y, Z) and three rotations (X, Y, Z). 'Free' means the component can move or rotate in that direction; 'Fixed' means it cannot.

CellValue
A1Component
B1Translation X
C1Translation Y
D1Translation Z
E1Rotation X
F1Rotation Y
G1Rotation Z
A2Part A
B2Free
C2Free
D2Free
E2Free
F2Free
G2Free
A3Part B
B3Fixed
C3Free
D3Fixed
E3Free
F3Fixed
G3Free
A4Part C
B4Fixed
C4Fixed
D4Fixed
E4Fixed
F4Fixed
G4Fixed
A5Degrees of Freedom
B5=COUNTIF(B2:G2,"Free")
B6=COUNTIF(B3:G3,"Free")
B7=COUNTIF(B4:G4,"Free")
Formula Trace
=COUNTIF(B2:G2,"Free")
Step 1: Range B2:G2 values = ["Free", "Free", "Free", "Free", "Free", "Free"]
Step 2: COUNTIF(range, "Free") counts how many cells equal "Free"
Cell Reference Map
    A       B       C       D       E       F       G
1 |Component|Trans X |Trans Y |Trans Z |Rot X   |Rot Y   |Rot Z   |
2 |Part A   | Free   | Free   | Free   | Free   | Free   | Free   |
3 |Part B   | Fixed  | Free   | Fixed  | Free   | Fixed  | Free   |
4 |Part C   | Fixed  | Fixed  | Fixed  | Fixed  | Fixed  | Fixed  |
5 |Degrees  | =COUNTIF(B2:G2,"Free") |       |       |       |       |       |
6 |Degrees  | =COUNTIF(B3:G3,"Free") |       |       |       |       |       |
7 |Degrees  | =COUNTIF(B4:G4,"Free") |       |       |       |       |       |
The formula in B5 counts 'Free' in B2:G2 for Part A. Similarly, B6 and B7 count for Part B and Part C respectively.
Result
    A       B       C       D       E       F       G
1 |Component|Trans X |Trans Y |Trans Z |Rot X   |Rot Y   |Rot Z   |
2 |Part A   | Free   | Free   | Free   | Free   | Free   | Free   |
3 |Part B   | Fixed  | Free   | Fixed  | Free   | Fixed  | Free   |
4 |Part C   | Fixed  | Fixed  | Fixed  | Fixed  | Fixed  | Fixed  |
5 |Degrees  | 6      |       |       |       |       |       |
6 |Degrees  | 3      |       |       |       |       |       |
7 |Degrees  | 0      |       |       |       |       |       |
The degrees of freedom for each part are counted and shown in column B. Part A has 6 free directions, Part B has 3, and Part C has none.
Sheet Trace Quiz - 3 Questions
Test your understanding
How many degrees of freedom does Part A have according to the formula?
A3
B6
C0
D5
Key Result
COUNTIF(range, "Free") counts how many directions are free for a component.

Practice

(1/5)
1. In SolidWorks, how many degrees of freedom does a new component have before applying any mates?
easy
A. 6 degrees of freedom
B. 3 degrees of freedom
C. 0 degrees of freedom
D. 9 degrees of freedom

Solution

  1. Step 1: Understand degrees of freedom in 3D space

    A component in 3D space can move along 3 axes and rotate about 3 axes, totaling 6 degrees of freedom.

  2. Step 2: Recall initial state of a new component

    Before any mates are applied, the component is free to move and rotate in all 6 ways.

  3. Final Answer:

    6 degrees of freedom -> Option A

  4. Quick Check:

    Initial freedom = 6 [OK]
Hint: Remember 3 translations + 3 rotations = 6 freedoms [OK]
Common Mistakes:
  • Confusing degrees of freedom with number of mates
  • Thinking zero means free movement
  • Assuming 3D space has only 3 freedoms
2. Which of the following is the correct way to describe a component with zero degrees of freedom in SolidWorks?
easy
A. The component is fully fixed and cannot move or rotate
B. The component can move freely in all directions
C. The component can only rotate but not translate
D. The component has unlimited degrees of freedom

Solution

  1. Step 1: Define zero degrees of freedom

    Zero degrees of freedom means no movement or rotation is possible.

  2. Step 2: Interpret what fully fixed means

    A fully fixed component cannot translate or rotate in any direction.

  3. Final Answer:

    The component is fully fixed and cannot move or rotate -> Option A

  4. Quick Check:

    Zero freedom = fully fixed [OK]
Hint: Zero freedom means no movement at all [OK]
Common Mistakes:
  • Thinking zero freedom means free movement
  • Confusing rotation freedom with translation freedom
  • Assuming partial movement is allowed
3. If a component initially has 6 degrees of freedom and you apply 3 mates that each restrict one degree of freedom, how many degrees of freedom remain?
medium
A. 9 degrees of freedom
B. 3 degrees of freedom
C. 0 degrees of freedom
D. 6 degrees of freedom

Solution

  1. Step 1: Start with initial degrees of freedom

    The component starts with 6 degrees of freedom.

  2. Step 2: Subtract degrees restricted by mates

    Each mate restricts one degree, so 3 mates restrict 3 freedoms.

  3. Step 3: Calculate remaining degrees of freedom

    6 - 3 = 3 degrees of freedom remain.

  4. Final Answer:

    3 degrees of freedom -> Option B

  5. Quick Check:

    6 - 3 = 3 [OK]
Hint: Subtract mates from 6 freedoms to find remaining [OK]
Common Mistakes:
  • Adding mates instead of subtracting
  • Assuming each mate restricts multiple freedoms
  • Confusing total freedoms with mates count
4. You applied 6 mates to a component, but it still moves. What is the most likely reason?
medium
A. The component has infinite degrees of freedom
B. You need to apply more mates to fix the component
C. Some mates are redundant and do not reduce degrees of freedom
D. SolidWorks does not support fixing components

Solution

  1. Step 1: Understand mate redundancy

    Some mates may overlap in restricting the same freedom, causing redundancy.

  2. Step 2: Recognize effect of redundant mates

    Redundant mates do not reduce additional degrees of freedom, so movement remains.

  3. Final Answer:

    Some mates are redundant and do not reduce degrees of freedom -> Option C

  4. Quick Check:

    Redundant mates don't fix movement [OK]
Hint: Check for redundant mates if component still moves [OK]
Common Mistakes:
  • Assuming more mates always fix movement
  • Ignoring mate redundancy
  • Believing SolidWorks cannot fix components
5. You have a component with 2 degrees of freedom left. You want to fully fix it by applying mates. Which combination of mates will correctly reduce the remaining freedoms?
hard
A. Apply 3 mates that restrict only one degree of freedom each
B. Apply 1 mate that restricts 2 degrees of freedom simultaneously
C. Apply 2 mates that restrict the same degree of freedom twice
D. Apply 2 mates that each restrict one unique degree of freedom

Solution

  1. Step 1: Identify remaining freedoms

    The component has 2 freedoms left to restrict.

  2. Step 2: Choose mates that restrict unique freedoms

    Each mate must restrict a different freedom to reduce total freedoms correctly.

  3. Step 3: Avoid redundant mates

    Applying mates that restrict the same freedom twice does not reduce freedoms further.

  4. Final Answer:

    Apply 2 mates that each restrict one unique degree of freedom -> Option D

  5. Quick Check:

    Unique mates reduce freedoms correctly [OK]
Hint: Use mates targeting different freedoms to fully fix [OK]
Common Mistakes:
  • Applying redundant mates on same freedom
  • Assuming one mate can restrict multiple freedoms
  • Applying more mates than needed without effect