kinematic chains - 2026 ACF Regionals

Packet I: Bonus 13

The number of degrees of freedom of one of these systems is related to the number of joints by the mobility formula. For 10 points each:

[10h] Name these idealized systems consisting of rigid bodies coupled together by joints.

ANSWER: kinematic chains [or linkages; prompt on mechanisms; prompt on chains]

[10m] If several of these statements for a kinematic chain are redundant, a kinematic chain that the mobility formula predicts to have zero degrees of freedom can still move. Joints are typically modelled as a holonomic one of these statements.

ANSWER: constraints [accept holonomic constraints; accept overconstrained systems or mechanisms]

[10e] Kinematic chains are commonly used to model the manipulators of these machines, which interact with their environment using an end-effector. These autonomous machines are capable of performing complex tasks.

ANSWER: robots [accept robotic manipulators]

<GC, Physics> | Packet I - McGill B, UCLA A, Michigan B, Georgia Tech C, Southampton B

Heard	PPB	E %	M %	H %
62	12.10	82%	32%	7%

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Conversion

Team	Opponent	Part 1	Part 2	Part 3	Total	Parts
Alabama A	Tennessee B	0	0	10	10	E
Berkeley A	Berkeley D	0	10	10	20	ME
Berkeley B	Stanford B	0	0	10	10	E
Berkeley C	Stanford A	0	10	10	20	ME
Binghamton B	Rochester	0	0	10	10	E
Brandeis B	Bowdoin A	0	0	0	0
Bristol	LSE	0	0	10	10	E
Brown	Bowdoin B	0	10	0	10	M
Bruin	WashU B	0	10	0	10	M
Cambridge B	Imperial A	0	0	10	10	E
Carleton College	Washington B	0	0	10	10	E
Central Florida A	Florida C	0	0	10	10	E
Central Florida C	Central Florida B	0	0	10	10	E
Chicago A	Purdue A	0	10	10	20	ME
Chicago C	Illinois B	0	0	10	10	E
Columbia A	Maryland A	0	0	10	10	E
Cornell A	Penn State	0	10	10	20	ME
Cornell B	RIT	0	0	10	10	E
Cornell C	Binghamton A	0	0	10	10	E
Dartmouth B	Southern Connecticut State	10	0	10	20	HE
Duke	William and Mary	0	0	0	0
Durham	City St. George's	0	0	10	10	E
Georgetown	Columbia C	0	0	10	10	E
Georgia Tech A	Minnesota A	0	10	10	20	ME
Georgia Tech B	Mississipi State	10	0	10	20	HE
Harvard A	Dartmouth A	0	0	10	10	E
Illinois A	Indiana A	10	0	0	10	H
Illinois C	Northwestern B	0	10	10	20	ME
Imperial C	Edinburgh B	0	10	0	10	M
Indiana B	Northwestern D	0	0	10	10	E
Iowa State	Claremont	0	10	10	20	ME
James Madison B	Liberty B	0	0	10	10	E
John Jay	Catholic	0	10	10	20	ME
Johns Hopkins A	NYU B	0	10	10	20	ME
Liberty C	James Madison A	0	0	10	10	E
Louisville A	Georgia Tech D	0	0	0	0
Louisville B	Kentucky	0	0	0	0
MIT	Brandeis A	10	10	10	30	HME
Maryland B	Vassar	0	0	10	10	E
McGill A	UBC B	0	10	10	20	ME
Missouri A	Washington A	0	0	10	10	E
NYU A	Columbia B	0	10	10	20	ME
NYU C	Johns Hopkins B	0	0	10	10	E
North Carolina B	NC State B	0	0	10	10	E
North Carolina C	NC State A	0	0	10	10	E
Northwestern C	Indiana C	0	0	0	0
Notre Dame A	Chicago B	0	0	10	10	E
Notre Dame B	Chicago E	0	0	10	10	E
Oxford A	Cambridge C	0	10	10	20	ME
Purdue B	Chicago D	0	0	10	10	E
Rutgers A	Rutgers B	0	0	0	0
South Carolina A	Liberty A	0	0	10	10	E
Swarthmore	Maryland C	0	0	10	10	E
Tennessee A	Sewanee	0	0	10	10	E
Texas A	Murray State A	0	10	10	20	ME
Texas B	Texas A&M A	0	0	10	10	E
UCL	Oxford B	0	0	10	10	E
VCU	South Carolina B	0	0	10	10	E
Vanderbilt B	WashU A	0	0	10	10	E
Virginia Tech A	North Carolina A	0	10	10	20	ME
Virginia Tech B	Virginia	0	10	0	10	M
Yale	Harvard B	0	10	10	20	ME

Summary

Tournament	Edition	Match	Heard	PPB	E %	M %	H %
California (North)	Main Site	✓	3	16.67	100%	67%	0%
Canada	Main Site	✓	1	20.00	100%	100%	0%
Florida	Main Site	✓	2	10.00	100%	0%	0%
Lower Mid-Atlantic	Main Site	✓	9	10.00	78%	22%	0%
Midwest	Main Site	✓	9	11.11	78%	22%	11%
Northeast	Main Site	✓	6	15.00	67%	50%	33%
Overflow	Main Site	✓	4	15.00	100%	50%	0%
South Central	Main Site	✓	2	15.00	100%	50%	0%
Southeast	Main Site	✓	7	8.57	57%	14%	14%
UK	Main Site	✓	6	11.67	83%	33%	0%
Upper Mid-Atlantic	Main Site	✓	9	12.22	89%	33%	0%
Upstate NY	Main Site	✓	4	12.50	100%	25%	0%